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1.	In a class of 1000 students, the ratio of boys to girls is 3 : 2. It is known that 88% of the boys passed, and 93% of the girls passed. Find the total no. of students who failed in this examination.1). 722). 543). 1004). 28
Answer» Total no. of students = 1000 Ratio of boys to GIRLS = 3 : 2 ⇒ No. of boys = $(\FRAC{3}{5}\; \times \;1000 = 600)$ ⇒ No. of girls = 1000 - 600 = 400 It is KNOWN that 88% of the boys passed ⇒ No. of boys passed = $(\frac{{88}}{{100}}\;\times\;600=528)$ ⇒ No. of boys failed = Total no. of boys – No. of boys passed = 600 – 528 = 72 Similarly, it is known that 93% of the girls passed ⇒ No. of girls passed = $(\frac{{93}}{{100}}\; \times \;400 = 372)$ ⇒ No. of girls failed = Total no. of girls – No. of girls passed = 400 – 372 = 28 So, Total No. of students failed = No. of boys failed + No. of girls failed ∴ Total No. of students failed = 72 + 28 = 100

In a class of 1000 students, the ratio of boys to girls is 3 : 2. It is known that 88% of the boys passed, and 93% of the girls passed. Find the total no. of students who failed in this examination.1). 722). 543). 1004). 28

Answer»

Total no. of students = 1000

Ratio of boys to GIRLS = 3 : 2

⇒ No. of boys = $(\FRAC{3}{5}\; \times \;1000 = 600)$

⇒ No. of girls = 1000 - 600 = 400

It is KNOWN that 88% of the boys passed

⇒ No. of boys passed = $(\frac{{88}}{{100}}\;\times\;600=528)$

⇒ No. of boys failed = Total no. of boys – No. of boys passed = 600 – 528 = 72

Similarly, it is known that 93% of the girls passed

⇒ No. of girls passed = $(\frac{{93}}{{100}}\; \times \;400 = 372)$

⇒ No. of girls failed = Total no. of girls – No. of girls passed = 400 – 372 = 28

So, Total No. of students failed = No. of boys failed + No. of girls failed

∴ Total No. of students failed = 72 + 28 = 100

Discussion

2.	If in a class test, A got 129.5 marks which are 70% of the B’s marks and B got 25% more marks than C while C got only 74% marks. Calculate the total number of marks for which the test was held.1). 1802). 2003). 1504). 250
Answer» A GOT 129.5 MARKS which is 70% of B’s marks ⇒ B’s marks = (129.5 × 100)/70 = 12950/70 = 185 B’s marks are 125% of C’s marks ⇒ C’s marks = (185 × 100)/125 = 18500/125 = 148 C got only 74% marks ⇒ TOTAL marks = (148 × 100)/74 = 14800/74 = 200 ∴ Total marks for which the test held is 200.

If in a class test, A got 129.5 marks which are 70% of the B’s marks and B got 25% more marks than C while C got only 74% marks. Calculate the total number of marks for which the test was held.1). 1802). 2003). 1504). 250

Answer»

A GOT 129.5 MARKS which is 70% of B’s marks

⇒ B’s marks = (129.5 × 100)/70 = 12950/70 = 185

B’s marks are 125% of C’s marks

⇒ C’s marks = (185 × 100)/125 = 18500/125 = 148

C got only 74% marks

⇒ TOTAL marks = (148 × 100)/74 = 14800/74 = 200

∴ Total marks for which the test held is 200.

Discussion

3.	There are five actors S, T, U, V and W in a play. The salary of S is Rs. 10000 and the salary of T is 25% less than the salary of U whose salary is 50% more than the salary of S. The salary of V is Rs. 20000 which is Rs. 6000 more than the salary of W. Average salary of three lowest paid actors is what percent of the average salary of the three highest paid actors?1). 80.80%2). 71.93%3). 67.45%4). 83.45%
Answer» Given, SALARY of S = Rs. 10000 Let salary of T, U and W be Rs. T, Rs. U and Rs. W respectively. Given, ⇒ U = 10000 + 10000 × 50/100 ⇒ U = 15000 Salary of U = Rs. 15000 ⇒ T = U - U × 25/100 ⇒ T = 15000 - 15000 × 25/100 ⇒ T = 11250 Salary of T = Rs. 11250 Given, Salary of V = Rs. 20000 ⇒ W = 20000 - 6000 ⇒ W = 14000 Salary of W = Rs. 14000 Three highest paid actors from this FIVE is W, U and V. Average salary of three highest paid actors = (14000 + 15000 + 20000)/3 = 49000/3 = 16333.33 Average salary of three lowest paid actors = (10000 + 11250 + 14000)/3 = 35250/3 = 11750 Required PERCENTAGE = (11750/16333.33) × 100 = 71.93%

There are five actors S, T, U, V and W in a play. The salary of S is Rs. 10000 and the salary of T is 25% less than the salary of U whose salary is 50% more than the salary of S. The salary of V is Rs. 20000 which is Rs. 6000 more than the salary of W. Average salary of three lowest paid actors is what percent of the average salary of the three highest paid actors?1). 80.80%2). 71.93%3). 67.45%4). 83.45%

Answer»

Given,

SALARY of S = Rs. 10000

Let salary of T, U and W be Rs. T, Rs. U and Rs. W respectively.

Given,

⇒ U = 10000 + 10000 × 50/100

⇒ U = 15000

Salary of U = Rs. 15000

⇒ T = U - U × 25/100

⇒ T = 15000 - 15000 × 25/100

⇒ T = 11250

Salary of T = Rs. 11250

Given,

Salary of V = Rs. 20000

⇒ W = 20000 - 6000

⇒ W = 14000

Salary of W = Rs. 14000

Three highest paid actors from this FIVE is W, U and V.

Average salary of three highest paid actors

= (14000 + 15000 + 20000)/3

= 49000/3

= 16333.33

Average salary of three lowest paid actors

= (10000 + 11250 + 14000)/3

= 35250/3

= 11750

Required PERCENTAGE

= (11750/16333.33) × 100

= 71.93%

Discussion