# Chain Rules - Online Quiz

Following quiz provides Multiple Choice Questions (MCQs) related to **Chain Rules**. You will have to read all the given answers and click over the correct answer. If you are not sure about the answer then you can check the answer using **Show Answer** button. You can use **Next Quiz** button to check new set of questions in the quiz.

Q 1 - If 4/5th of a cistern is filled in 1 minute, how much more time will be required to fill the rest of it?

### Answer : B

### Explanation

Let the required time be x seconds. Part filled = 4/5, Remaining part = (1- 4/5 ) = 1/5. Less part to be filled , less is the time taken (direct) 4/5 :1/5 :: 60 : x ⇒ 4/5 * x = (1/5 * 60 ) = 12 ⇒ x= (12 * 5/4 ) = 15. Required time = 15 seconds.

Q 2 - 3 men or 5 women can finish a piece of work in 12 days. How long will 6 men and 5 women take to finish the work?

### Answer : A

### Explanation

3 men = 5 women ⇒ 6 men =10 women ⇒ (6 men +5 women )= 15 women. Let the required number of days be x. More women , less days (Indirect) 15 : 5 :: 12 : x ⇒ 15x = (5* 12 ) ⇒ x= (5*12)/15 = 4 days

Q 3 - 8 men can complete a piece of work in 12 days ; 4 women can complete it in 48 days and 10 children can complete the same piece of work in 24 days . In how many days can 10 men , 4 women and 10 children complete the same piece of work?

### Answer : D

### Explanation

1 man can complete the work in ( 12 * 8) = 96 days. 1 women can complete the work in ( 48 * 4) = 192 days. 1 child can complete the work in ( 24 * 10) = 240 days. 1 men 1 days work = 1/96, 1 women1 days work = 1/192. 1 child 1 days work = 1/240. ( 10 men + 4 women + 10 children) 1 days work = ( 10/ 96 + 4/192 + 10/240) = (5/48 + 1 /48 + 1/24) = 8/48 = 1/6. ∴ They will do the work in 6 days.

Q 4 - A man and a boy working together can complete a work in 24 days . If for the last 6 days man alone the work , then it is completed in 26 days. How long will the boy take to complete the work alone?

### Answer : A

### Explanation

Let 1 men 1 days work be 1/x and 1 boy 1 days work be 1/y Then, 1/x + 1/y = 1/24 20/x + 20 / y + 6 /x )1 ⇒ 20 (1/x + 1/y) + 6/x = 1 ⇒ (20 * 24) + 6/x = 1 ⇒ 6/x = (1- 20/24) = 4 / 24 = 1/6 ⇒ 1/x = 1/ 36 ⇒ 1/y = ( 1/24 - 1/ 36 ) = 1/72. ∴ The boy along will do it in 72 days.

Q 5 - Two persons can complete a piece of work in 9 days. How many more persons are needed to complete double the work in 12 days?

### Answer : A

### Explanation

Let the required number of persons be x . More work, more persons (direct) More days , less persons (Indirect) Work 1:2 :: 2 : (2+x) Days 12:9 1*12 * ( 2 + x ) = (2 * 9 *2 ) ⇒ ( 2 + x ) = 36/12 = 3 ⇒ x=1.

Q 6 - Four examiners can examine a certain number of answer papers in 10 days by working for 5 hours a day. For how many hours in a day would 2 examiners have to work in order to examine twice the number of answer papers in 20 days?

### Answer : D

### Explanation

Let the number of hours per days be x. More days, less hours per days ( Indirect) Less examiners , more hours per days ( Indirect) More Ans. Books , more hours per days ( direct) Days 20 : 10 Examiners 2 : 4 :: 5 : x Ans. Books 1 : 2 ∴ (20 * 2 * 1 * x) = ( 10 * 4 * 2* 5 ) ⇒ x = 400 / 40 = 10 hrs per days.

Q 7 - 8 men working for 9 hours a day complete a piece of work in 20 days . In how many days can 7 men working for 10 hours a day complete the same piece of work?

### Answer : D

### Explanation

Let the required number of days be x . Less men , more days ( Indirect) More working hours, less days (Indirect) Men 7: 8 :: 20 : x Working hrs 10 : 9 ∴ ( 7 * 10 * x ) = ( 8 * 9 * 20) ⇒ x = 8 * 9 * 20 / 7 * 10 = 144/7 = 144/7.

Q 8 - If the rent for grazing 40 cows for 20 days in Rs 740, how many cows can graze for 30 days on Rs 222?

### Answer : B

### Explanation

Let the required number of cows be x. Less rent, less cows (Direct) More days, less cows (Indirect) Rent 740 : 222 :: 40 : x Days 30: 20 ∴ ( 740 * 30 * x) = ( 222 * 20 * 40 ) ⇒ x = 222* 20 * 40 / 740 * 30 = 8 cows.

Q 9 - 2 men and 7 boys can do a piece of work in 14 days ; 3 men and 8 boys can do the same in 11 days . 8 men and 6 boys can do 3 times the amount of this work in

### Answer : A

### Explanation

Let 1 men 1 days work be 1/x and 1 boy 1 day work be 1/y Then 2/x + 7/y = 1/14 ⇒ 2u + 7v = 1/14 -(i) When u= 1/x, v=1/y. 3/x +8/y =1/11 ⇒ 3u + 8v = 1/11?.(ii) Multiplying (i) by (ii) by 2 and subtracting , we get: 5v = ( 3/14 ? 2/11) = 5/ 154 ⇒ v = 1/154 Putting v = 1/154 in (i) we get : 2u +7* 1/154 = 1/14 ∴ 2u = (1/14- 1/22)= (11-7/54) = 4/154 = 2/77 ⇒ u=1/77. (8 men +6 boys) 1 days work = (8/77 +6/154 ) = 22/154 = 1/7. ∴ 8men and 6 boys can do it in 7 days. They will do thrice of this work in (3*7) days = 21days.

Q 10 - 20 men complete one third of a piece of work in 20 days. How many more men should be employed to finish the rest of the work in 25 more days?

### Answer : B

### Explanation

Work done = 1/3, Remaining work = (1- 1/3 ) = 2/3 Let the number of additional men be x. More work, more men (Direct) More days , less men (Indirect) Work 1/3 : 2 /3 :: 20 : (20 +x) Days 25:20 1/3 * 25 * ( 20 + x) = 2 /3 * 20 *20 ⇒ (20 +x) = 32 ⇒ x=12. Required number of days = 12.