227 + Interview Questions in QUANTITATIVE APTITUDE in PROFIT AND LOSS Page 5 InterviewSolution

201.	A man sells an article at a profit of 19%. If the had bought it at 30% less and sold it for Rs.42 less, he would have gained 50%. Find the cost price of the article1). Rs. 2102). Rs. 703). Rs. 1404). Rs. 300
Answer» Let the cost price of the article be C. Initial selling price = $(\left( {1 + \frac{{19}}{{100}}} \right)C = 1.19 C)$ If the cost price had been 30% less, we have Revised cost price = $(C\left( {1 - \frac{{30}}{{100}}} \right) = \frac{7}{10}C = 0.7 C)$ Revised selling price = 1.19C - 42 New profit percentage = $(\frac{{\left( {1.19C - 42} \right) - 0.7C}}{{0.7C}} = \frac{{0.49C - 10.5}}{{0.7C}} )$ GIVEN, this figure is 50%. $(\Rightarrow \frac{{0.49C - 42}}{{0.7C}} = \frac{{50}}{{100}})$ ⇒ 49 C – 4200 = 35 C ⇒ 14 C = 4200 ⇒ C = 300

201.

A man sells an article at a profit of 19%. If the had bought it at 30% less and sold it for Rs.42 less, he would have gained 50%. Find the cost price of the article1). Rs. 2102). Rs. 703). Rs. 1404). Rs. 300

Answer»

Let the cost price of the article be C.

Initial selling price = $(\left( {1 + \frac{{19}}{{100}}} \right)C = 1.19 C)$

If the cost price had been 30% less, we have

Revised cost price = $(C\left( {1 - \frac{{30}}{{100}}} \right) = \frac{7}{10}C = 0.7 C)$

Revised selling price = 1.19C - 42

New profit percentage = $(\frac{{\left( {1.19C - 42} \right) - 0.7C}}{{0.7C}} = \frac{{0.49C - 10.5}}{{0.7C}} )$

GIVEN, this figure is 50%.

$(\Rightarrow \frac{{0.49C - 42}}{{0.7C}} = \frac{{50}}{{100}})$

⇒ 49 C – 4200 = 35 C

⇒ 14 C = 4200

⇒ C = 300

Discussion

202.	Rekha invested Rs. 8000 in a business. After 8 months, Maya invested Rs. 6000 in the same business. At the end of second year, if Rekha received Rs. 2000 as her share of profit, how much money did Maya received as his share of profit?1). Rs. 25002). Rs. 5003). Rs. 10004). Rs. 1500
Answer» REKHA’s investment = RS. 8000 for 24 months Maya’s investment = Rs. 6000 for (24 – 8) = 16 months Hence, at the end of second year, (Rekha’s share of profit)? (Maya’s share of profit) = (8000 × 24)? (6000 × 16) ⇒ 2000? (Maya’s share of profit) = 2 ⇒ Maya’s share of profit = 2000/2 = Rs. 1000 ∴ At the end of second year, Maya received Rs. 1000 as her share of profit

202.

Rekha invested Rs. 8000 in a business. After 8 months, Maya invested Rs. 6000 in the same business. At the end of second year, if Rekha received Rs. 2000 as her share of profit, how much money did Maya received as his share of profit?1). Rs. 25002). Rs. 5003). Rs. 10004). Rs. 1500

Answer»

REKHA’s investment = RS. 8000 for 24 months

Maya’s investment = Rs. 6000 for (24 – 8) = 16 months

Hence, at the end of second year,

(Rekha’s share of profit)? (Maya’s share of profit) = (8000 × 24)? (6000 × 16)

⇒ 2000? (Maya’s share of profit) = 2

⇒ Maya’s share of profit = 2000/2 = Rs. 1000

∴ At the end of second year, Maya received Rs. 1000 as her share of profit

Discussion

203.	By selling 200 pencils, a shopkeeper gains the selling price of 40 pencils. His gain percent is:1). 25%2).3). 15%4). 12%
Answer» LET SP of 1 PENCILS be I rupee Then SP of 200 pencils is Rs 200× 1 = Rs 200 Gain = 40 × 1 = Rs 40 CP = SP – gain = 200 – 40 = 160 Gain% =Gain/CP × 100 = 40/160 × 100 % = 25%

203.

By selling 200 pencils, a shopkeeper gains the selling price of 40 pencils. His gain percent is:1). 25%2).3). 15%4). 12%

Answer»

LET SP of 1 PENCILS be I rupee

Then SP of 200 pencils is Rs 200× 1 = Rs 200

Gain = 40 × 1 = Rs 40

CP = SP – gain = 200 – 40 = 160

Gain% =Gain/CP × 100 = 40/160 × 100 % = 25%

Discussion

204.	If toffees are bought at the rate of 7 for Rs. 6, at what rate per hundred must they be sold to gain 33%?1). Rs. 1142). Rs. 1153). Rs. 1184). Rs. 120
Answer» Chocolates are bought at a rate of 7 for Rs. 6. ∴ Cost price of one Chocolate = Rs. 6/7. Let’s assume that the Chocolates are sold at a rate of 100 for Rs. X. ∴ Selling price of one Chocolate = Rs. X/100 According to the information GIVEN in the problem, there’s a profit is of 33% in this transaction. % profit $(= \frac{{selling\;price - cost\;price}}{{cost\;price}} \times 100)$ $(\BEGIN{ARRAY}{l} \therefore 33 = \frac{{\left( {\frac{X}{{100}}} \right) - \left( {\frac{6}{7}} \right)}}{{\left( {\frac{6}{7}} \right)}} \times 100\\ \Rightarrow \left( {\frac{{33}}{{100}} \times \frac{6}{7}} \right) + \frac{6}{7} = \frac{X}{{100}}\\ \Rightarrow \frac{{198}}{{700}} + \frac{6}{7} = \frac{X}{{100}}\\ \Rightarrow \frac{{198 + 600}}{{700}} = \frac{X}{{100}}\\ \Rightarrow X = \frac{{798}}{{700}} \times 100 = 114 \END{array})$ ∴ Chocolates should be sold at a rate of 100 for Rs. 114.

204.

If toffees are bought at the rate of 7 for Rs. 6, at what rate per hundred must they be sold to gain 33%?1). Rs. 1142). Rs. 1153). Rs. 1184). Rs. 120

Answer»

Chocolates are bought at a rate of 7 for Rs. 6.

∴ Cost price of one Chocolate = Rs. 6/7.

Let’s assume that the Chocolates are sold at a rate of 100 for Rs. X.

∴ Selling price of one Chocolate = Rs. X/100

According to the information GIVEN in the problem, there’s a profit is of 33% in this transaction.

% profit $(= \frac{{selling\;price - cost\;price}}{{cost\;price}} \times 100)$

$(\BEGIN{ARRAY}{l} \therefore 33 = \frac{{\left( {\frac{X}{{100}}} \right) - \left( {\frac{6}{7}} \right)}}{{\left( {\frac{6}{7}} \right)}} \times 100\\ \Rightarrow \left( {\frac{{33}}{{100}} \times \frac{6}{7}} \right) + \frac{6}{7} = \frac{X}{{100}}\\ \Rightarrow \frac{{198}}{{700}} + \frac{6}{7} = \frac{X}{{100}}\\ \Rightarrow \frac{{198 + 600}}{{700}} = \frac{X}{{100}}\\ \Rightarrow X = \frac{{798}}{{700}} \times 100 = 114 \END{array})$

∴ Chocolates should be sold at a rate of 100 for Rs. 114.

Discussion

205.	A milk vendor purchased some milk at the rate of Rs. 14 per litre and after mixing 25% of water to the whole mixture, He sold the mixture at Rs 14 per litre. His profit per cent is.1). 35%2). 30%3). 25%4). 14%
Answer» Let the amount of milk initially purchased be x litres. TOTAL C.P. of x litres of milk =Rs. 14X ? 25% of WATER is added to it, the volume of water added to milk = 25% of x = (25/100) × x = x/4 litres ∴ Final volume of MIXTURE $(= \;x\; + \;\frac{x}{4} = \;\frac{{5x}}{4}litres)$ According to the information given in the question, 5x/4 litres of mixture is sold at Rs. 14 PER litre ∴ total S.P. of the mixture $(= \frac{{5x}}{4} \times 14 = \;\frac{{35x}}{2} =)$Rs. 17.5x We know that, % Profit $(= \frac{{S.P.\; - C.P.}}{{C.P.\;}} \times 100)$ ⇒ % Profit $(= \frac{{17.5x\; - \;14x}}{{14x\;}} \times 100)$ ⇒ % Profit = 25

205.

A milk vendor purchased some milk at the rate of Rs. 14 per litre and after mixing 25% of water to the whole mixture, He sold the mixture at Rs 14 per litre. His profit per cent is.1). 35%2). 30%3). 25%4). 14%

Answer»

Let the amount of milk initially purchased be x litres.

TOTAL C.P. of x litres of milk =Rs. 14X

? 25% of WATER is added to it, the volume of water added to milk = 25% of x

= (25/100) × x = x/4 litres

∴ Final volume of MIXTURE $(= \;x\; + \;\frac{x}{4} = \;\frac{{5x}}{4}litres)$

According to the information given in the question,

5x/4 litres of mixture is sold at Rs. 14 PER litre

∴ total S.P. of the mixture $(= \frac{{5x}}{4} \times 14 = \;\frac{{35x}}{2} =)$Rs. 17.5x

We know that, % Profit $(= \frac{{S.P.\; - C.P.}}{{C.P.\;}} \times 100)$

⇒ % Profit $(= \frac{{17.5x\; - \;14x}}{{14x\;}} \times 100)$

⇒ % Profit = 25

Discussion

206.	Two shirts are bought at the rate of Rs. 400 each. Shopkeeper sells one at the profit of 50% and other at the loss of 50%. What will be the total profit or loss in the whole transaction?1). Loss of Rs. 502). No profit/loss3). Profit of Rs. 254). Loss of Rs. 150
Answer» Total cost PRICE = 2 × 400 = Rs. 800 When he sells a profit of 150%, SELLING price = 400 + 50% of 400 = Rs. 600 When he sells at a loss of 150%, Selling price = 400 – 50% of 400 = Rs. 200 Total selling price = 600 + 200 = Rs. 800 Now, as total selling price and cost price is same so overall there is no profit and no loss

206.

Two shirts are bought at the rate of Rs. 400 each. Shopkeeper sells one at the profit of 50% and other at the loss of 50%. What will be the total profit or loss in the whole transaction?1). Loss of Rs. 502). No profit/loss3). Profit of Rs. 254). Loss of Rs. 150

Answer»

Total cost PRICE = 2 × 400 = Rs. 800

When he sells a profit of 150%,

SELLING price = 400 + 50% of 400 = Rs. 600

When he sells at a loss of 150%,

Selling price = 400 – 50% of 400 = Rs. 200

Total selling price = 600 + 200 = Rs. 800

Now, as total selling price and cost price is same so overall there is no profit and no loss

Discussion

207.	The cost price of an article was Rs. 1,560. If the dealer wanted to earn a profit of 10% after giving a discount of 30%, the marked price should be1). Rs. 2,4512). Rs. 2,4003). Rs. 2,4204). Rs. 2,200
Answer» If the DEALER wants a profit of 10%, SELLING Price = 1,560 + 10% of 1,560 = 1,716 According to the given CONDITION, the above cost is obtained after giving 30% discount on Marked price Let the marked price be ‘X’ ∴ x – 30% of x = 1,716 ∴ 0.7x = 1,716 ∴ x ≈ 2451 ∴ The marked price of the ARTICLE is Rs. 2,451

207.

The cost price of an article was Rs. 1,560. If the dealer wanted to earn a profit of 10% after giving a discount of 30%, the marked price should be1). Rs. 2,4512). Rs. 2,4003). Rs. 2,4204). Rs. 2,200

Answer»

If the DEALER wants a profit of 10%, SELLING Price = 1,560 + 10% of 1,560 = 1,716

According to the given CONDITION, the above cost is obtained after giving 30% discount on Marked price

Let the marked price be ‘X’

∴ x – 30% of x = 1,716

∴ 0.7x = 1,716

∴ x ≈ 2451

∴ The marked price of the ARTICLE is Rs. 2,451

Discussion

208.	1). 10002). 11003). 9804). 1150
Answer» DISCOUNT % = (MP - SP)/MP × 100 Let the MARKED PRICE be Rs. x New price after first discount = x - (10/100) × x = Rs. 0.9x Price after SUCCESSIVE discount = 0.9x - (30/100) × 0.9x = Rs. 0.63x 0.63x = 630 ⇒ x = 1000 Marked price = Rs. 1000

208.

1). 10002). 11003). 9804). 1150

Answer»

DISCOUNT % = (MP - SP)/MP × 100

Let the MARKED PRICE be Rs. x

New price after first discount = x - (10/100) × x = Rs. 0.9x

Price after SUCCESSIVE discount = 0.9x - (30/100) × 0.9x = Rs. 0.63x

0.63x = 630 ⇒ x = 1000

Marked price = Rs. 1000

Discussion

209.	A man sells an article at a proﬁt of 35%. If he had bought it for 15% less price and sold it for Rs. 32 less, then he would have gained 40%. What is the initial cost price (in Rs) of the article?1). 2502). 2003). 3004). 400
Answer» Case 1: Let the cost price be ‘C’ Since the man sold the article at a profit of 35% ⇒ Selling Price (S) = Cost Price × (1 + Profit%) = C × (1 + 35%) = 1.35C ⇒ S = 1.35C---- (Equation 1) Case 2: In case the cost price is 15% less = C - (15%C) = C - 0.15C = 0.85C ⇒ Selling Price = S - 32 ⇒ Selling Price = Cost Price × (1 + Profit%) ⇒ S - 32 = 0.85C × (1 + 40%)---- (Equation 2) Substituting the VALUE of ‘S’ from Equation 1 in Equation 2, we get ⇒ 1.35C - 32 = 0.85C (1.4) ⇒ 1.35C - 32 = 1.19C ⇒ 1.35C - 1.19C = 32 ⇒ 0.16C = 32 ⇒ C = 32/0.16 = 200 ∴ Initial Cost price = 200

209.

A man sells an article at a proﬁt of 35%. If he had bought it for 15% less price and sold it for Rs. 32 less, then he would have gained 40%. What is the initial cost price (in Rs) of the article?1). 2502). 2003). 3004). 400

Answer»

Case 1:

Let the cost price be ‘C’

Since the man sold the article at a profit of 35%

⇒ Selling Price (S) = Cost Price × (1 + Profit%) = C × (1 + 35%) = 1.35C

⇒ S = 1.35C---- (Equation 1)

Case 2:

In case the cost price is 15% less = C - (15%C) = C - 0.15C = 0.85C

⇒ Selling Price = S - 32

⇒ Selling Price = Cost Price × (1 + Profit%)

⇒ S - 32 = 0.85C × (1 + 40%)---- (Equation 2)

Substituting the VALUE of ‘S’ from Equation 1 in Equation 2, we get

⇒ 1.35C - 32 = 0.85C (1.4)

⇒ 1.35C - 32 = 1.19C

⇒ 1.35C - 1.19C = 32

⇒ 0.16C = 32

⇒ C = 32/0.16 = 200

∴ Initial Cost price = 200

Discussion

210.	Mr. Sanjay Sharma, a businessman had some income in the year 2000, such that he earned a profit of 20% on his investment in the business. In the year 2001, his investment was less by Rs. 5 lakh but still had the same income (Income = Investment + Profit) as that in year 2000. Thus the percent Profit earned in year 2001 increased by 6% percentage point. What was his investment in year 2000?1). Rs. 102000002). Rs. 105000003). Rs. 150500004). Data inadequate
Answer» Let the INVESTMENT be a. Given, a businessman had some income in the year 2000, such that he earned a profit of 20% on his investment in the business. In the year 2001, his investment was less by RS. 5 lakh but STILL had the same income (Income = Investment + Profit) as that in year 2000. The profit INCREASE by 6%. a + 20% of a = a – 500000 + 26% of (a – 500000) 1.2a = 1.26a – 1.26 × 500000 ⇒ 0.06a = 1.26 × 500000 ⇒ a = Rs. 10500000

210.

Mr. Sanjay Sharma, a businessman had some income in the year 2000, such that he earned a profit of 20% on his investment in the business. In the year 2001, his investment was less by Rs. 5 lakh but still had the same income (Income = Investment + Profit) as that in year 2000. Thus the percent Profit earned in year 2001 increased by 6% percentage point. What was his investment in year 2000?1). Rs. 102000002). Rs. 105000003). Rs. 150500004). Data inadequate

Answer»

Let the INVESTMENT be a.

Given, a businessman had some income in the year 2000, such that he earned a profit of 20% on his investment in the business. In the year 2001, his investment was less by RS. 5 lakh but STILL had the same income (Income = Investment + Profit) as that in year 2000. The profit INCREASE by 6%.

a + 20% of a = a – 500000 + 26% of (a – 500000)

1.2a = 1.26a – 1.26 × 500000

⇒ 0.06a = 1.26 × 500000

⇒ a = Rs. 10500000

Discussion

211.	1). 15%2). 14.15%3). 16.5%4). 17%
Answer» From the given data, TOTAL cost of the land = Rs. (18 + 3) LAKHS = Rs. 21 lakhs Selling PRICE of the land = Rs. 24.57 ⇒ Profit = selling price - cost price = 24.57 - 21 = Rs. 3.57 lakhs ⇒ Profit percentage = profit/cost price × 100 = 3.57/21 × 100 = 17%

211.

1). 15%2). 14.15%3). 16.5%4). 17%

Answer»

From the given data,

TOTAL cost of the land = Rs. (18 + 3) LAKHS = Rs. 21 lakhs

Selling PRICE of the land = Rs. 24.57

⇒ Profit = selling price - cost price = 24.57 - 21 = Rs. 3.57 lakhs

⇒ Profit percentage = profit/cost price × 100 = 3.57/21 × 100 = 17%

Discussion

212.	P, Q and R started a business by investing the money in the ratio 4 ∶ 3 ∶ 5. P left the business after 6 months and R left after 8 months. The profit at the end of the year is 5/9th of total investment. Find the amount of investment done by P, if the profit share by R is Rs. 40000.1). Rs. 480002). Rs. 600003). Rs. 720004). Rs. 75000
Answer» P, Q and R started a business by INVESTING the money in the RATIO 4 ? 3 ? 5. P left the business after 6 MONTHS and R left after 8 months; ∴ Profit sharing ratio = (4 × 6) ? (3 × 12) ? (5 × 8) = 12 ? 18 ? 20 Since profit share by R is Rs. 40000; ∴ Total profit = 40000 × 50/20 = Rs. 100000 Since profit at the end of the year is 5/9^th of total investment done; ∴ Total investment = 100000 × 9/5 = Rs. 180000 ∴ Investment done by P = 180000 × 4/12 = Rs. 60000

212.

P, Q and R started a business by investing the money in the ratio 4 ∶ 3 ∶ 5. P left the business after 6 months and R left after 8 months. The profit at the end of the year is 5/9th of total investment. Find the amount of investment done by P, if the profit share by R is Rs. 40000.1). Rs. 480002). Rs. 600003). Rs. 720004). Rs. 75000

Answer»

P, Q and R started a business by INVESTING the money in the RATIO 4 ? 3 ? 5. P left the business after 6 MONTHS and R left after 8 months;

∴ Profit sharing ratio = (4 × 6) ? (3 × 12) ? (5 × 8) = 12 ? 18 ? 20

Since profit share by R is Rs. 40000;

∴ Total profit = 40000 × 50/20 = Rs. 100000

Since profit at the end of the year is 5/9^th of total investment done;

∴ Total investment = 100000 × 9/5 = Rs. 180000

∴ Investment done by P = 180000 × 4/12 = Rs. 60000

Discussion

213.	Two friends bought 100 articles and divided them on a condition such that each will have to sell his share at a profit % numerically equal to number of articles. In what ratio should they divide the articles to earn an overall profit of 58%.1). 3 : 72). 4 : 53). 5 : 74). 2 : 3
Answer» Let FIRST person took x article and other took (100 – x) And price of each article is 100 x article will be SOLD at a profit of x% and (100 – x) article will be sold at a profit of (100 – x)% So, overall profit = 58x100 = [(x)(x) + (100 – x) (100 – x)] 58 × 100 = x² + 10000 + x² - 200x x² - 100x + 2100 = 0 x = 30, 70 So, the RATIO of their article is 3: 7 Short trick To save time, USE option method: Let the first person has 30 article then other has 70 ⇒ (30 × 30 + 70 × 70)/100 = 5800/100 = 58%

213.

Two friends bought 100 articles and divided them on a condition such that each will have to sell his share at a profit % numerically equal to number of articles. In what ratio should they divide the articles to earn an overall profit of 58%.1). 3 : 72). 4 : 53). 5 : 74). 2 : 3

Answer»

Let FIRST person took x article and other took (100 – x)

And price of each article is 100

x article will be SOLD at a profit of x% and (100 – x) article will be sold at a profit of (100 – x)%

So, overall profit = 58x100 = [(x)(x) + (100 – x) (100 – x)]

58 × 100 = x² + 10000 + x² - 200x

x² - 100x + 2100 = 0

x = 30, 70

So, the RATIO of their article is 3: 7

Short trick

To save time, USE option method:

Let the first person has 30 article then other has 70

⇒ (30 × 30 + 70 × 70)/100 = 5800/100 = 58%

Discussion

214.	1). 20%2). 17%3). 21½%4). 25%
Answer» TOTAL C.P of 120 chalks = 120 × 10 = 1200 Now total C.P of 60 chalks = 600 S.P = C.P + profit S.P = 600 + 15 × 600/100 S.P = 600 + 90 = 690 Now for a total gain of 20%, Total S.P = 1200 + 20% of 1200 Total S.P = 1200 + 20/100 of 1200 Total S.P = 1200 + 240 = 1440 60 chalks are sold at S.P of 690 Hence so as to make a overall gain of 20%, S.P of remaining 60 chalks should be = (1440 – 690) = 750 Hence profit made on other 60 chalks = 750 – 600 = 150 % gain = 150 × 100/600 = 25%

214.

1). 20%2). 17%3). 21½%4). 25%

Answer»

TOTAL C.P of 120 chalks = 120 × 10 = 1200

Now total C.P of 60 chalks = 600

S.P = C.P + profit

S.P = 600 + 15 × 600/100

S.P = 600 + 90 = 690

Now for a total gain of 20%, Total S.P = 1200 + 20% of 1200

Total S.P = 1200 + 20/100 of 1200

Total S.P = 1200 + 240 = 1440

60 chalks are sold at S.P of 690

Hence so as to make a overall gain of 20%, S.P of remaining 60 chalks should be = (1440 – 690) = 750

Hence profit made on other 60 chalks = 750 – 600 = 150

% gain = 150 × 100/600 = 25%

Discussion

215.	1). 60%2). 55%3). 51%4). 47%
Answer» For successive DISCOUNT, Successive discount = (-a) + (-b) + (-a)(-b)/100 Here, a = 30%, b = 30% ∴ Successive discount OFFERED = (-30) + (-30) + (900/100) = -60 + 9 = -51%

215.

1). 60%2). 55%3). 51%4). 47%

Answer»

For successive DISCOUNT,

Successive discount = (-a) + (-b) + (-a)(-b)/100

Here, a = 30%, b = 30%

∴ Successive discount OFFERED = (-30) + (-30) + (900/100) = -60 + 9 = -51%

Discussion

216.	A retailer purchases a sofa set at a discount of 20% and sells it for Rs. 2200. In the bargain he makes a profit of 20%. How much discount (in Rs.) did he receive?1). 13752). 68753). 7854). 458
Answer» Let the M.P of the SOFA set be RS. x Then, C.P for the RETAILER = M.P – 20% of M.P ⇒ C.P = x – 20x/100 ⇒ C.P = 80x/100 The retailer sells it at Rs. 2200 and makes a profit of 20%. S.P = C.P + profit ⇒ 2200 = 80x/100 + 20% of 80x/100 ⇒ 2200 = 96x/100 ⇒ x = 6875/3 Thus, M.P = 6875/3 DISCOUNT offered was 20%. ⇒ discount = 20% of 6875/3 = 1375/3 ∴ discount = Rs. 458.33 ≈ Rs. 458

216.

A retailer purchases a sofa set at a discount of 20% and sells it for Rs. 2200. In the bargain he makes a profit of 20%. How much discount (in Rs.) did he receive?1). 13752). 68753). 7854). 458

Answer»

Let the M.P of the SOFA set be RS. x

Then, C.P for the RETAILER = M.P – 20% of M.P

⇒ C.P = x – 20x/100

⇒ C.P = 80x/100

The retailer sells it at Rs. 2200 and makes a profit of 20%.

S.P = C.P + profit

⇒ 2200 = 80x/100 + 20% of 80x/100

⇒ 2200 = 96x/100

⇒ x = 6875/3

Thus, M.P = 6875/3

DISCOUNT offered was 20%.

⇒ discount = 20% of 6875/3 = 1375/3

∴ discount = Rs. 458.33 ≈ Rs. 458

Discussion

217.	In the year 2014, the marked price of the laptop was Rs. 85,000. The marked price gets depreciated by 15% every year. In year 2017, dealer found that there were 15 laptops available from the order of 2015. He sold those laptops at the marked price of year 2017. The total amount of loss faced by the dealer is?1). Rs. 2005012). Rs. 2722013). Rs. 2900014). Rs. 300741
Answer» GIVEN Principal = Rs. 85000 Rate of interest per annum (R) = 15% Time period (n) = 1 year Amount of depreciation under compound interest (A) = P [(1 - (n/100)]ⁿ ⇒ Amount = 85000 [(1 - (15/100)]¹ ⇒ Amount = 85000 × (1 - 0.15) ⇒ Amount = 85000 × 0.85 ⇒ Amount for laptop in year 2015 = Rs. 72250 To calculate the amount for the laptop in year 2017, Principal = Rs. 85000 Rate of interest per annum (r) = 15% Time period (n) = 3 year Amount = 85000 [(1 - (15/100)]³ ⇒ Amount = 85000 × (1 - 0.15)³ ⇒ Amount = 85000 × 0.85³ ⇒ Amount = 85000 × 0.614125 ⇒ Amount of laptop in year 2017 = Rs. 52200.625 Loss on SELLING of 1 laptop = Rs. (72250 - 52200.625) = Rs. 20049.375 Total loss in selling of 15 laptops = 20049.375 × 15 = Rs. 300741 (approx.) ∴ Total loss occur = Rs. 300741

217.

In the year 2014, the marked price of the laptop was Rs. 85,000. The marked price gets depreciated by 15% every year. In year 2017, dealer found that there were 15 laptops available from the order of 2015. He sold those laptops at the marked price of year 2017. The total amount of loss faced by the dealer is?1). Rs. 2005012). Rs. 2722013). Rs. 2900014). Rs. 300741

Answer»

GIVEN Principal = Rs. 85000

Rate of interest per annum (R) = 15%

Time period (n) = 1 year

Amount of depreciation under compound interest (A) = P [(1 - (n/100)]ⁿ

⇒ Amount = 85000 [(1 - (15/100)]¹

⇒ Amount = 85000 × (1 - 0.15)

⇒ Amount = 85000 × 0.85

⇒ Amount for laptop in year 2015 = Rs. 72250

To calculate the amount for the laptop in year 2017,

Principal = Rs. 85000

Rate of interest per annum (r) = 15%

Time period (n) = 3 year

Amount = 85000 [(1 - (15/100)]³

⇒ Amount = 85000 × (1 - 0.15)³

⇒ Amount = 85000 × 0.85³

⇒ Amount = 85000 × 0.614125

⇒ Amount of laptop in year 2017 = Rs. 52200.625

Loss on SELLING of 1 laptop = Rs. (72250 - 52200.625) = Rs. 20049.375

Total loss in selling of 15 laptops = 20049.375 × 15 = Rs. 300741 (approx.)

∴ Total loss occur = Rs. 300741

Discussion

218.	Ramesh sells an article at a loss of 5%. If he buys it for 30% less price and sells it for Rs. 38.5 less, then his profit will be 20%. What is the cost price (in Rs.) of the article?1). 4502). 3003). 3504). 250
Answer» Let the CP of an article be 100x SP of the article = cost price - LOSS% of cost price = 100x - 5% of 100x = 95x ⇒ New CP of the article = 100x - 30% of 100x = 100x - 30X = 70x ⇒ New SP of the article = 70x + 20% of 70x = 70x + 14x = 84X According to the question ⇒ 84x = 95x - 38.5 ⇒ 11x = 38.5 ⇒ x = 3.5 ∴ CP of the article = 100 × 3.5 = 350

218.

Ramesh sells an article at a loss of 5%. If he buys it for 30% less price and sells it for Rs. 38.5 less, then his profit will be 20%. What is the cost price (in Rs.) of the article?1). 4502). 3003). 3504). 250

Answer»

Let the CP of an article be 100x

SP of the article = cost price - LOSS% of cost price = 100x - 5% of 100x = 95x

⇒ New CP of the article = 100x - 30% of 100x = 100x - 30X = 70x

⇒ New SP of the article = 70x + 20% of 70x = 70x + 14x = 84X

According to the question

⇒ 84x = 95x - 38.5

⇒ 11x = 38.5

⇒ x = 3.5

∴ CP of the article = 100 × 3.5 = 350

Discussion

219.	1). 8002). 9003). 7504). 1000
Answer» Let, Cost Price of the first table = Rs. y ∴ Cost price of the other table = Rs. (1800 - y) [? Purchase price of TWO tables = Rs.1800] According the problem, Selling price of the first table = Rs. y × 4/5 Selling price of the SECOND table = Rs. ((1800 - y) × 5) /4 ∴ $(\frac{{4y}}{5}\; + \;\frac{{\left( {1800 - y} \right)\; \times \;5}}{4})$ = 1800 + 90 [? He made an overall gain of Rs. 90] Or, $(\frac{{4y}}{5} - \frac{{5y}}{4})$ = 1890 - 2250 Or, (16y - 25y) /20 = - 360 Or, - 9y = - 360 × 20 Or, y = 7200/9 ⇒ y = 800 ∴ Cost of the first table = Rs. 800 Cost of the other table = Rs. (1800 - 800) = Rs. 1000 ∴ Cost of the LESSER valued chair = Rs. 800

219.

1). 8002). 9003). 7504). 1000

Answer»

Let, Cost Price of the first table = Rs. y

∴ Cost price of the other table = Rs. (1800 - y) [? Purchase price of TWO tables = Rs.1800]

According the problem,

Selling price of the first table = Rs. y × 4/5

Selling price of the SECOND table = Rs. ((1800 - y) × 5) /4

∴ $(\frac{{4y}}{5}\; + \;\frac{{\left( {1800 - y} \right)\; \times \;5}}{4})$ = 1800 + 90 [? He made an overall gain of Rs. 90]

Or, $(\frac{{4y}}{5} - \frac{{5y}}{4})$ = 1890 - 2250

Or, (16y - 25y) /20 = - 360

Or, - 9y = - 360 × 20

Or, y = 7200/9

⇒ y = 800

∴ Cost of the first table = Rs. 800

Cost of the other table = Rs. (1800 - 800) = Rs. 1000

∴ Cost of the LESSER valued chair = Rs. 800

Discussion

220.	1). 65 2/3%2). 66 2/3%3). 67 2/3%4). 68 2/3%
Answer» Given, selling price (SP) of 9 articles is equal to the cost price (CP) of 15 articles 9 × SP = 15 × CP ∴ SP = 5CP/3 ∴ % PROFIT $(= \;\frac{{\frac{{5CP}}{3} - CP}}{{CP}} \times 100\% \; = \;\frac{{200}}{3}\% \; = \;66\frac{2}{3}\% )$

220.

1). 65 2/3%2). 66 2/3%3). 67 2/3%4). 68 2/3%

Answer»

Given, selling price (SP) of 9 articles is equal to the cost price (CP) of 15 articles

9 × SP = 15 × CP

∴ SP = 5CP/3

∴ % PROFIT $(= \;\frac{{\frac{{5CP}}{3} - CP}}{{CP}} \times 100\% \; = \;\frac{{200}}{3}\% \; = \;66\frac{2}{3}\% )$

Discussion

221.	In an alloy, gold and silver are in the ratio of 2 : 3. In the second alloy, the same elements are in the ratio of 4 : 5. If these two alloys be mixed to form a new alloy in which two elements are in the ratio of 7 : 8, the ratio of these two alloys in new alloys is?1). 1 : 22). 1 : 33). 1 : 44). 1 : 7
Answer»

Discussion

222.	By selling 3 dozen Apple, a vendor loses the selling price of 4 Apple. His loss percent is :1). \(12\frac{1}{2}\% \)2). \(11\frac{1}{9}\% \)3). 10%4). None of these
Answer» Let the SELLING PRICE of an apple = RS x ⇒ The selling price of 36 Apples = 36 × x = 36x ⇒ The Selling Price of 4 Apples = 4 × x = 4x ? When 36 Apples were sold the loss was equivalent to Selling price of 4 Apples ⇒ Loss = COST Price - Selling Price ⇒ 4x = Cost Price - 36x ⇒ Cost Price = 40x ⇒ Loss% = Loss/(Cost price) × 100 = (4x/40x) × 100 = 10%

222.

By selling 3 dozen Apple, a vendor loses the selling price of 4 Apple. His loss percent is :1). $12\frac{1}{2}\% $2). $11\frac{1}{9}\% $3). 10%4). None of these

Answer»

Let the SELLING PRICE of an apple = RS x

⇒ The selling price of 36 Apples = 36 × x = 36x

⇒ The Selling Price of 4 Apples = 4 × x = 4x

? When 36 Apples were sold the loss was equivalent to Selling price of 4 Apples

⇒ Loss = COST Price - Selling Price

⇒ 4x = Cost Price - 36x

⇒ Cost Price = 40x

⇒ Loss% = Loss/(Cost price) × 100 = (4x/40x) × 100 = 10%

Discussion

223.	A discount of 45% on an article is equal to the discount of 65% on other article. What is the respective ratio of the marked price of both the articles?1). 5 : 92). 3 : 43). 7 : 124). 13 : 9
Answer» Let MP of first article = X And MP of other article = y Then, according to the QUESTION, x × 45% = y × 65% ⇒ x/y = 65/45 ⇒ x : y = 13 : 9 ∴ RESPECTIVE ratio of the marked PRICE of both the articles = 13 : 9

223.

A discount of 45% on an article is equal to the discount of 65% on other article. What is the respective ratio of the marked price of both the articles?1). 5 : 92). 3 : 43). 7 : 124). 13 : 9

Answer»

Let MP of first article = X

And MP of other article = y

Then, according to the QUESTION,

x × 45% = y × 65%

⇒ x/y = 65/45

⇒ x : y = 13 : 9

∴ RESPECTIVE ratio of the marked PRICE of both the articles = 13 : 9

Discussion

224.	The marked price of an article is 60% more than its cost price. If the article is sold for Rs. 300 after offering a discount of Rs. 20, then what will be the profit percentage?1). 402). 503). 254). 45
Answer» SP of the ARTICLE = 300 MP of the article = 300 + 20 = 320 Let CP of the article = 100% MP of the article = 100% + 60% = 160% ⇒ 160% ≡ RS. 320 ⇒ (CP) = 100% ≡ Rs. 200 ∴ PROFIT % = (200 - 100)/200 × 100 = 50%

224.

The marked price of an article is 60% more than its cost price. If the article is sold for Rs. 300 after offering a discount of Rs. 20, then what will be the profit percentage?1). 402). 503). 254). 45

Answer»

SP of the ARTICLE = 300

MP of the article = 300 + 20 = 320

Let CP of the article = 100%

MP of the article = 100% + 60% = 160%

⇒ 160% ≡ RS. 320

⇒ (CP) = 100% ≡ Rs. 200

∴ PROFIT % = (200 - 100)/200 × 100 = 50%

Discussion

225.	The cost price of an article is Rs. 800. After allowing a discount of 10%, a gain of 12.5% was made. Then the marked price of the article is1). Rs. 1,0002). Rs. 1,1003). Rs. 1,2004). Rs. 1,300
Answer» Let, The marked PRICE of the article is ‘x’. After ALLOWING a discount of 10%, Price at which it is sold = x – 0.10x = 0.90x. ACCORDING to the question, The COST price = Rs.800. Gain made = 12.5%. ∴ 0.90x = 800 + 0.125 × 800 ⇒ 0.90x = 900 ⇒ x = 1000.

225.

The cost price of an article is Rs. 800. After allowing a discount of 10%, a gain of 12.5% was made. Then the marked price of the article is1). Rs. 1,0002). Rs. 1,1003). Rs. 1,2004). Rs. 1,300

Answer»

Let, The marked PRICE of the article is ‘x’.

After ALLOWING a discount of 10%,

Price at which it is sold = x – 0.10x = 0.90x.

ACCORDING to the question,

The COST price = Rs.800.

Gain made = 12.5%.

∴ 0.90x = 800 + 0.125 × 800

⇒ 0.90x = 900

⇒ x = 1000.

Discussion

226.	If bananas are bought at the rate of 4 for a rupee, how many must be sold for a rupee so as to gain 33\(\frac{1}{3}\%\)1). 2.52). 23). 34). 4
Answer» S. P. of 4 BANANAS $(= \left[ {100 + \frac{{100}}{3}} \right]\% )$ of Rs. 1 = Rs. $(\frac{{400}}{{300}} = {\rm{Rs}}.{\rm{\;}}\frac{4}{3})$ Number of bananas sold for Rs. $(\frac{4}{3})$ = 4 Number of bananas sold for Rs. 1 $(= \frac{4}{4} \times 3 = 3)$

226.

If bananas are bought at the rate of 4 for a rupee, how many must be sold for a rupee so as to gain 33$\frac{1}{3}\%$1). 2.52). 23). 34). 4

Answer»

S. P. of 4 BANANAS $(= \left[ {100 + \frac{{100}}{3}} \right]\% )$ of Rs. 1

= Rs. $(\frac{{400}}{{300}} = {\rm{Rs}}.{\rm{\;}}\frac{4}{3})$

Number of bananas sold for Rs. $(\frac{4}{3})$ = 4

Number of bananas sold for Rs. 1 $(= \frac{4}{4} \times 3 = 3)$

Discussion

227.	A man invested Rs. 8000 for a year in the share market. At the end of the year, he gained 15% and he invested the amount for the second year. At the end of the second year, he suffered a loss of 15%. Find the gain or loss per cent in the investment after two years.1). 5.25% gain2). 5.25% loss3). 2.25% loss4). 2.25% gain
Answer» ⇒ Amount after one year with 15% GAIN = 8000 x 115/100 = RS. 9200⇒ Amount after 2ND year with a loss of 15% = Rs. 9200 x 85/100 ⇒ Amount after 2nd year with a loss of 15% = Rs. 7820 ⇒ Loss percent = (8000 – 7820)/8000 x 100 ⇒ Loss percent = 2.25% ∴ the loss percentage is of 2.25 %

227.

A man invested Rs. 8000 for a year in the share market. At the end of the year, he gained 15% and he invested the amount for the second year. At the end of the second year, he suffered a loss of 15%. Find the gain or loss per cent in the investment after two years.1). 5.25% gain2). 5.25% loss3). 2.25% loss4). 2.25% gain

Answer»

⇒ Amount after one year with 15% GAIN = 8000 x 115/100 = RS. 9200⇒ Amount after 2ND year with a loss of 15% = Rs. 9200 x 85/100

⇒ Amount after 2nd year with a loss of 15% = Rs. 7820

⇒ Loss percent = (8000 – 7820)/8000 x 100

⇒ Loss percent = 2.25%

∴ the loss percentage is of 2.25 %

Discussion

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