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Given:

Expenditure on medical = 10% of his income

Expenditure on traveling = 20% of his income

The expenditure left = Rs. 3500

Calculation:

Let the total income be 100%

The left expenditure = 100% – (10% + 20%)

⇒ 100% – 30%

⇒ 70%

Now,

By using unitary method

70% = 3500

⇒ 1% = 3500/70

⇒ 1% = 50

⇒ 100% = 100 × 50

⇒ 100% = 5000

∴ The total income of person will be Rs. 5000

(a) Ratio of Expenses = 4 : 2 : 5,
therefore amount spend on clothes, i.e. 2x = 5540
∴ x = 2770
Total exp = (4 + 2 + 5)x = 11x
= 11 × 2770
Total income be x.
55% of x = 30470

x=30470*100/20 =55400

Given

Naveena spent Rs. 1,800 on a dress and Rs. 3,270 on books and notebooks

She still was left with 35% of the total amount she had originally.

Concept used

In these question the percentage of amount is 100%

Calculation

Let the amount be 100%

⇒ 1800 + 3270 + 35% = 100%

⇒ 65% = 5070

⇒ 1% =78

⇒ 100% = 7800

∴ The total amount she had orginally is Rs.7800

(d) Total valid votes = 85% of 15200 = 12920
 Number of valid votes to other candidate
= 45% of 12920 = 5814

Calculation:

In 2010, Let the salary of Ramesh, Ganesh and Rajesh be 6x, 5x and 7x

Ramesh's salary increased by 25% during 2010 - 2015 = 6x × 125/100

⇒ 7.5x

But in 2015 the salaries ratio is 3 : 4 : 3 for Ramesh, Ganesh and Rajesh respectively

We can see in 2015, the salary of Ramesh and Rajesh is the same which is in the given ratio.

So, In 2015, the salary for Rajesh should also be 7.5x

Now percentage increase in the salary for Rajesh during 2010 - 2015 = [(7.5x - 7x)/7x] × 100

⇒ (0.5/7) × 100

⇒ 50/7

⇒ 7.14%

∴ The percentage increase in Rajesh’s salary during this period is closest to 7%.

Given:

Since, X% of Y = Y × (X/100)

⇒ XY/100

⇒ 1% of XY

And Y% of X = X × (Y/100)

⇒ 1% of XY

⇒ (X% of Y) + (Y% of X) = 2% of XY

∴ The required value is 2% of XY

Given:

The literate population is 80% 

Total population of the city = 8500

Calculations:

Total literate population = 8500 × 80/100 = 6800

Total illiterate population = 8500 – 6800 = 1700

∴ Total illiterate population is 1700 

Given:

15% of water bill is reduced from the original bill

Balance to be paid = Rs. 170

Calculations:

Let the original bill be Rs. x

⇒ x – (15/100)x = 170

⇒ (100 – 15)x/100 = 170

⇒ 85x/100 = 170

⇒ x/100 = 2

⇒ x = Rs. 200 

∴ The original bill was Rs. 200

GIVEN:

The list price of a TV is Rs. 22500.

GST = 15%

FORMULA USED:

X% of Y = Y × X/100

CALCULATION:

GST amount on the TV = 22500 × 15/100 = Rs. 3375

Hence,

Total value paid by the customer = 22500 + 3375 = Rs. 25875

Calculation:

40% of (a – b) = 20% of (a + b)

⇒ (40 / 100) of (a – b) = (20/100) of (a + b)

⇒ 40 × (a – b) = 20 × (a + b)

⇒ 2(a – b) = (a + b)

⇒ 2a – 2b = a + b

⇒ a = 3b

⇒ a = 3, b = 1

 Required percentage = (1/3) × 100%

= 100/3%

= 33.33%

∴ b is 33.33% of a

Given:

Fall of shares = 25%

Due to fall in the share one can buy 12 shares more than before by investing Rs. 16,200

Calculation:

Let original price of a share be 100x

So, new price of a share = 100x × 75/100 = 75x

According to the question,

Here, 25% reduction of rate allowed 12 more shares at Rs. 16,200

⇒ (16,200/75x) – (16,200/100x) = 12

⇒ 216/x – 162/x = 12

⇒ 54 = 12x

⇒ x = 4.5

Original price of a shares = 100x = 450

∴ Original price of a shares is Rs. 450

Given:

Percentage increase in the price of diesel = 26%

Percentage increase in total expenditure = 15%

Concept used:

P × C = E

Where P is Price, C is Consumption and E is expenditure

Calculation:

Let initial price be P1, consumption be C1, and expenditure be E1 

P1 × C1 = E1 

⇒ C1 = E1/P1

Let new price be P2, new quantity consumed be C2, and new expenditure be E2 

P₂ = P₁ + 26% of P₁ 

⇒ P2 = 1.26P₁ 

E₂ = E₁ + 15% of E₁ 

⇒ E2 = 1.15E₁ 

As, P₂ × C₂ = E₂ 

⇒ 1.26P1 × C₂ = 1.15E1 

⇒ C₂ = (1.15E₁)/(1.26P₁)

⇒ C2 = 0.9126 × E₁/P₁ 

⇒ C₂ = 0.9126C₁ 

Decrease in consumption = C₁ – C₂ 

⇒ Decrease in consumption = C₁ – 0.9126C1 = 0.0874C₁ 

Percentage decrease in consumption = (Decrease in consumption/Initaial consumption) × 100

⇒ Percentage decrease in consumption = (0.0874C₁/C₁) × 100

∴ The percentage decrease in consumption is 8.7% (correct to 1 decimal place)

Given:

Salary of Chirashree increased by 25%

Present expenditure is Rs. 20000

Present savings is Rs. 5000 less than expenditure

Concept:

Total income (salary) is sum of savings and expenditure

Formula:

Old salary = New salary × 100/(100 + x)

Where x = increment percent

Calculation:

Present savings = Rs. (20000 – 5000) = Rs. 15000

Present salary = Rs. (15000 + 20000) = Rs. 35000

Previous salary = 35000 × 100/125 = Rs. 28000

∴ Previous salary of Chirashree was Rs. 28000

Given:

Initial salary = Rs. 7000

Increased salary = Rs. 12,000

Calculation:

Increase in salary = Rs. 12000 – Rs. 7000 = Rs. 5000

Increase % in salary = (5000/7000) × 100 

\(\Rightarrow 71\frac{3}{7}\)%

∴ The percentage increase in the salary is \(71\frac{3}{7}\)%

Given:

Initial salary = Rs. 8100

Increased salary = Rs. 9000

Formula used:

Percentage increased = (Initial salary – Increased salary)/Initial salary × 100

Calculation:

Initial salary = Rs. 8100

Increased salary = Rs. 9000

Percentage increased = (Initial salary – Increased salary)/Initial salary × 100

⇒ Required percent = (9000 – 8100)/8100 × 100

⇒ Required percent = 900/8100 × 100

⇒ Required percent = 1/9 × 100

⇒ Required percent = 100/9%

⇒ Required percent = \(11\frac{1}{9}\% \)

Given:

Population of town = 2000

Percentage of men = 40%

Percentage of women = 35%

Calculation:

Percentage of children = 100% – (40% + 35%)

⇒ 100% – 75%

⇒ 25%

Number of children = 25% of 2000

⇒ (25/100) × 2000

⇒ 500

∴ The number of children is 500

Given:

Percentage of boys = 70%

Total number of girls = 255

Calculation:

Percentage of girls = (100 – 70)%

⇒ 30%

According to the question,

⇒ 30% = 255

⇒ 70% = (255/30%) × 70%

⇒ 595

∴ The number of boys is 595

Given:

Ratio of girls to boys = 5 : 3

Total capacity of class = 48

Percentage of girls absent = 16.67%

Calculation:

Number of girls in the class = [5/(5 + 3)] × 48

⇒ (5/8) × 48

⇒ 30

Now, number of girls present = [1 - (16.67/100)] × 30

⇒ [1 - (1/6)] × 30

⇒ (5/6) × 30

⇒ 25

∴ 25 girls are present in the class.

16.67% = 100/600 = 1/6

Given:

Price of an article has increased by 30%

Increase in expenditure = 17%

Formula used:

Ratio Method

As, Expenditure = (Price × Consumption)

⇒ Consumption = (Expenditure/Price)

Calculation:

Let us assume the initial price of the article be = 100x

After increasing, the final price = 130x

Also, the Expenditure of the article increased by 17% 

Let us assume the initial Expenditure be = 100y

After increment, The final Expenditure be = 117y

After Cross Multiplication we get,

Ratio of consumption,

⇒ 100y × 130x : 117y × 100x

⇒ 10 :  9

Percentage change in Consumption = (10 – 9)/10 = (1/10) × 100 = 10% Decrease

∴ The percentage change in the consumption of the article is 10%

Given:

1,50,000 is distributed among A,B and C

They receive 20%,30% and 50% respectively

Calculation:

Amount receive by A = (20/100) × 1,50,000

= Rs.30,000

Amount receive by B = (30/100) × 1,50,000

= Rs.45,000

Amount receive by C = (50/100) × 1,50,000

= Rs.75,000

Now

A receives the same amount from another sum which is 50% of the total amount

⇒ Rs. 30,000 is 50% of another amount sum

⇒ 2nd amount is Rs.60,000

Also

 B receives 30% of 2nd amount

⇒ (30/100) × 60,000

= Rs.18,000

∴ Total amount received by B is Rs.45,000 + Rs.18,000 i.e Rs.63,000

Given∶

Minimum percent to pass = 44

Marks scored = 80

Calculation∶

44% of x = 80 + 30

⇒ 44x/100 = 110

⇒ x = (110 × 100)/44

⇒ x = 250

Formula used 

Percentage = (required number/actual number) × 100 

Calculation 

⇒ Grams in 1 Kg = 1000g 

⇒ Required % = (137/1000) × 100 = 13.7% 

∴ The required answer is 13.7%

Given:

80% of the registered voters cast their votes in election, A wins 800 votes B 

Assumption :

Let the votes received by A be x  and B be y.

Calculation :

According to question,

⇒ x - y = 800 -------- (1)

Also 

⇒ (87.5/100)x = Y+ (12.5/100)x -------- (2)

⇒ y = (3/4)x -------- (3)

Eq(3) to solve (1) we get

⇒ x - (3/4)x = 800

⇒ x = 3200 and y = 2400

Now, We know that A & B collectively won 80% of total votes of total votes.

If the total number of registered voters in the village be z 

Then , (80/100)z = 3200 + 2400

⇒ z = (5600 × 5)/4

⇒ z = 7000

∴ Total number of registered voters in village are 7000

Given:

When the required number is reduced by 10% gives 27 as result.

Concept Used:

Concept of percentage. It is calculated on the basis of 100

For example, x% means x out of 100

Calculation:

Let, the required number be x

After reducing by 10% the given number reduced to (100 - 10)x/100

⇒ 9x/10

Accordingly,

9x/10 = 27

⇒ x = 30

∴ The required number is 30.

Calculation:

⇒ Let be  votes received by A = x and B = y

⇒ x - y = 400            (1)

⇒ also \(\frac{{87.5}}{{100}}x = y + \left( {\frac{{12.5}}{{100}}} \right)x\)         (2)

The votes lost by A would go into B's account solving (2) , we get 

⇒\(y = \frac{3}{4}x\)       (3)                                                                                                                                                                                                                                             

⇒ \(x - \frac{3}{4}x = 400\)

⇒ x = 1600 and y = 1200

Now, we know that A & B collectively won 70% of total votes.

If the total number of registered voters in the village be Z, 

Then, 70% Z = 1600 + 1200 

⇒ 70% Z = 2800

⇒ Z = 4000

∴ Z = 4000

Given:

25% of (P + Q) = 75% of (P - Q)

Calculations:

Solving the given equation,

⇒ (25/100) × (P + Q) = (75/100) × (P - Q)

⇒ (1/4) × (P + Q) = (3/4) × (P - Q)

⇒ (P + Q) = 3 × (P - Q)

⇒ P + Q = 3P - 3Q

⇒ 2P = 4Q

⇒ P = 2Q

⇒ P/Q = 2/1

∴ The value of P ∶ Q is 2 ∶ 1

Given:

Percentage of expenditure = 50%

Expenditure = Rs. 2000

Calculation:

50% = Rs. 2000

⇒ 100% = Rs. (2000/50%) × 100%

⇒ Rs. 4000

∴ His total earnings is Rs. 4000

Given:

Students failed in school X = 30%

Number of students in school Y = 150% more than number of students in school X

Students passed in both schools = 80%

Calculation:

Let number of students in school X be 100x

Number of failed students in school X = 30% of 100x

= 30x

Number of passes students in school Y = (100x – 30x)

= 70x

Number of students in school Y = 100x + 150% of 100x

= 100x + 150x = 250x

Total number of students in school X and school Y = 100x + 250x

= 350x

Number of passes students in both schools = 80% of 350x

= 280x

So, number of passed students in school Y = 280x – 70x

= 210x

Number of failed students in school Y = 250x –  210x

= 40x

Percentage of failed students in school Y = (40x/250x) × 100%

= 16%

∴ The percentage of students who failed from school Y is 16%

Formula used:

Area of rectangle = length × breadth

Calculation:

Let the length and breadth of a rectangle be l and b respectively

Initial area of rectangle = l × b

New length = l + 5% of l = 1.05 l

New area of rectangle = 1.05 l × b

Increase in area = (1.05 l × b) – (l × b) = 0.05 × l × b

Percentage increase = (0.05 × l × b)/(l × b) × 100 = 5%

∴ The area of rectangle will increase by 5%

Given:

A / B = 90 / 100 = 9 / 10

B / C = 115 / 100 = 23 / 20

Concept:

Calculate the ratio of A, B and C. Then, using the ratio values, calculate the % difference.

Calculation:

A / B = 9 / 10

B / C = 23 / 20

⇒ A ∶ B ∶ C = 207 ∶ 230 ∶ 200

∴ A - C = 207 - 200 = 7

Given:

If earning of A increases by 80%, he will save 50% of his income.

B’s income is Rs. 1000 less than the new income of A.

B saves Rs. 12000 and spends 25% more than he saves.

Formula Used:

Ratio of Profit = Ratios of product of invested amount and time

Income – expenditure = savings

Calculation:

Let 100x be the initial earning of A

New earnings of A = 180x

Savings of A = 180x × ½

Savings of A = 90x

Income of B = 180x – 1000

B saves Rs. 12000

B spends = Rs. (12000 × 5/4) = Rs. 15000

⇒ 180x – 1000 – 15000 = 12000

⇒ x = 1400/9

Savings of A = 90x = Rs. (90 × 1400/9) = Rs. 14000

∴ A’s savings is Rs.14000

GIVEN:

In two successive years, 100 and 200 students of a school appeared at the final examination. Respectively 80% and 60% of them passed.

FORMULA USED:

X% of Y = Y × X/100

CALCULATION:

Total number of students appeared in 2 years = 100 + 200 = 300

And

Total number of passed students in 2 years = 100 × 0.8 + 200 × 0.6

= 80 + 120

= 200

Hence,

Given:

Cost of shirt = Rs. 350

Percentage increase in cost = 10%

Concept:

Percentage Increase = (100 + x)%

Solution:

Let the increased cost of shirt be Rs. x.

Cost of shirt = Rs. 350

Percentage increase in cost = 10%

⇒ New cost = 110% of Previous cost

⇒ x = 110/100 × 350

⇒ x = 385

∴ The new cost of shirt is Rs. 385.

Short Trick/Topper's Approach:

Percentage increase in cost = 10%

⇒ New cost : Previous cost = 11 : 10      [10% = 1/10]

Previous cost of shirt = Rs. 350

⇒ 1 unit = 350/10 = 35

⇒ New cost of shirt = Rs. 11 × 35

⇒ New cost of shirt = Rs. 385

∴ The new cost of shirt is Rs. 385.

Given:

The income of Ravi is 50% more than Lalit’s income

Their expenditures are in the ratio 5 : 3.

Calculation:

Income of Ravi = (100 + 50)/100 of Lalit’s income

⇒ Ravi/Lalit = 3/2

Let income of Ravi and Lalit be 3x and 2x respectively

Also, their expenditure is 5y and 3y

Now, according to equation,

⇒ 3x – 5y = 2000      ----(1)

⇒ 2x – 3y = 2000      ----(2)

Now, Multiplying equation (1) by 3 and equation (2) by 5.

⇒ 9x – 15y = 6000       ----(3)

⇒ 10x – 15y = 10000      ----(4)

Now, subtract from equation (4) from equation (3)

⇒ x = 4000

Then, income of Ravi = 3x = 3 × 4000

⇒ Rs. 12,000

∴ Ravi’s income is Rs. 12,000 rupees.

Initial value = 60000

Final value = 40000

Diffrence = 60000 - 40000 = 20000

Required percentage change = 20000/60000 × 100 = 1/3 × 100 = 33(1/3)%

(a) No. of boys this year = 610 × 80% = 488
No. of girls = 488 × 175% = 854

Given∶

Original cost = Rs. 4,00,000

New cost = Rs. 4,80,000

Formula used∶

Increase percent = [(increase value / original value) × 100]%

Calculation:

Increase percent = [(increase value / original value) × 100]%

⇒ [(80,000 / 400000) × 100]%

⇒ 20%

∴ The percent increase in its cost is 20%.

Given∶

25% of a number is 1100.

Calculation∶

Let the number is x.

(25 / 100) × x = 1100

⇒ x = (1100 × 100) / 25

⇒ x = 4400

So, 10% of 4400 = 440

Given∶

A number exceeds 36% of itself by 768

Calculation∶

Let the number is x.

According to question∶

⇒ x = 36% of x + 768

⇒ x - (36x/100) = 768

⇒ 64x/100 = 768

⇒ x = 1200

Given:

In an election, a candidate secures 40% of the votes but is defeated by the only other candidate by a majority of 2980 votes.

Calculations:

Let the total votes polled be x 

other candidate got 60% of the votes.

According to the question,

(60 – 40)% of x = 2980

⇒ (20/100) × x = 2980 

⇒ x = 2980 × 5 = 14900

∴ the total number of votes recorded is 14900.

Given:

20% spent to room rent, 10% Remaining salary and Rs. 3600 gives to brother

Calculation:

Let Ram monthly income be = 100

According to question,

Room rent expenditure = (100 -20)

⇒ 80

Remaining amount groceries   expenditure = 80 of 10%

⇒ 8

Remaing amount gives his brother = {100 - (20 - 8)

⇒ 72

Giving to, 

⇒ 3600 = 72

⇒ 50

⇒ Total monthly income is 50 × 100 

⇒ 5,000

∴ Total monthly income is Rs. 5,000

Given:

Percentage spent on travelling = 20%

Percentage spent on groceries = 30%

Money left = Rs. 2500

Concept Used:

Total income = 100%

Calculations:

Total income = Rs. x

Percentage spent on travelling = 20%

Percentage spent on groceries = 30%

Percentage of money left = 100% – (20% + 30%) = 50%

⇒ Money left = Rs. 2500

50% = Rs. 2500

⇒ 100% = Rs. 2500 × 100%/50%

⇒ 100% = Rs. 5000

Total income = x = Rs. 5000

∴ The total income of the person is Rs. 5000.

Calculations:

Let us say that initially there were 100 commuters.

The distribution of different modes would be a below.

⇒ Car in Jan 2019 = 30% of 100 = 30

⇒ Bus in Jan 2019 = 20% of 100 = 20

⇒ Two Wheelers in Jan 2019 = 10% of 100 = 10

⇒ Metro in Jan 2019 = 40% of 100 = 40

Now, in Feb the total commuters have increased by 50%,

so total commuters in Feb 2019 = 100 + 50% of 100 = 150

⇒ Car in Feb 2019 = 30 + 33.33% of 30 = 40

⇒ Bus in Feb 2019 = 20 + 100% of 20 = 40

⇒ Two Wheelers in Feb 2019 = 10 + 100% of 10 = 20

⇒ Metro in Feb 2019 = 150 - (40 + 40 + 20) = 50

Change in metro = 50 - 40 = 10 

Percentage change in metro = (10/40) × 100 = 25% 

∴ Percentage change in metro is 25%.

Given:

20% of P = 30% of Q = 1/6 of R

Calculation:

Let 20/100 × P = 30/100 × Q = 1/6 × R = k

⇒ P/5 = 3Q/10 = R/6 = k

⇒ P = 5k

⇒ Q = 10k/3

⇒ R = 6k

∴ P : Q : R = 5k : 10k/3 : 6k

⇒ 15k : 10k : 18k = 15 :10 : 18

∴ The correct answer is 15 : 10 : 18

Given:

Increase in radius of cone = 30%

Increased in height of cone = 20%

Formula used:

V = (1/3) × π × r² × h

where,

V = volume of cone

r = radius of cone

h = height of cone

Calculations:

Let the initial radius and height of the cone be r, h.

Initial volume = (1/3) × π × r2 × h

New radius = r + (r × 30%)

⇒ 13r/10

New height =  h + (h × 20%)

⇒ 6h/5

New volume = (1/3) × π × (13r/10)2 × (6h/5)

⇒ (1/3) × π × (169r²/100) × (6h/5)

⇒ (1/3) × π × r2 × h × (169/100) × (6/5)

⇒ (Initial volume) × (169/100) × (6/5)

(New volume)/(Initial volume) = 507/250

∴ The ratio of new volume to initial volume is 507 : 250.

Calculation:

⇒ (2/5) × 70 = 28

⇒ (28/560) × 100 = 5%

∴ Two – fifth of 70 is 5% 560.