# 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 - 10 men can finish the construction of a wall in 8 days. How many men are added to finish the work in half a day?

### Answer : D

### Explanation

Let the total number of men be x. Less days , more men required (Indirect) 1/2 : 8 :: 10 : x ⇒ 1/2 x =(8* 10 )⇒ x= (8* 10* 2*) = 160. Number of men to be added = (160- 10 )=150.

Q 3 - 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 number of more men to be employed 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) = 800/25 = 32 ⇒ x = (32-20) = 12.

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 - Running at the same constant rate , 6 identical machines can produce 2700 bottle per minute . At this rate , how many bottles could 10 such machines produce in 4 minutes?

### Answer : B

### Explanation

Let the required number of bottles be x . More machines, more bottles ( Direct) More time, more bottles ( Direct) Machines 6 : 10 :: 2700 : x Time 1:4 (6 * 1 * x) = 10 * 4 * 2700 ) ⇒ 10 * 4 * 2700 / 6 = 1800 bottles.

Q 8 - If 42 persons consume 144kg of rice in 15 days , then in how many days will 30 persons consume 48kg of rice?

### Answer : D

### Explanation

Let the required number of days be x. More persons, more days (Direct) Less rice, less days (Indirect) Persons 30 : 42 :: 15 : x Quantity 144 : 48 ∴ ( 30 * 144 * x ) = ( 42 * 48 *15 ) ⇒ x = 42 * 48 * 15/ 30 * 144 = 7 days

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 - A garrison had provision for a certain number of days . After 10 days , 1/5 th of the men desert and it is found that the provision will now last just as long as before. How long was that?

### Answer : D

### Explanation

Initially, let x men had provisions for y days. Then, x men had provisions for (y-10) days. (x- x/5) men had provisions for y days. ∴ x ( y-10) = 4x /5 *y ⇒5xy - 50 x = 4xy ⇒ xy - 50x = 0 ⇒ x (y-50) = 0 ⇒ y = 50.