Chain Rules - Online Quiz



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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.

Questions and Answers

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?

A - 20 seconds

B - 15 seconds

C - 12 seconds

D - 10 seconds

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?

A - 160

B - 100

C - 120

D - 150

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?

A - 10

B - 12

C - 15

D - 20

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?

A - 72 days

B - 20 days

C - 24 days

D - 36 days

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?

A - 1

B - 2

C - 3

D - 4

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?

A - 15/2 hours

B - 8 hours

C - 7/2 hours

D - 10 hours

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?

A - 648

B - 1800

C - 2700

D - 10800

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?

A - 4

B - 5

C - 6

D - 7

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

A - 21 days

B - 18 days

C - 24 days

D - 36 days

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?

A - 35 days

B - 15 days

C - 25 days

D - 50 days

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.


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