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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 - A rope makes 140 rounds of the circumference of a cylinder, the radius of whose base is 14cm . How many times can it go rounds a cylinder with radius 20 cm?

Answer : C

Explanation

Let the required number   of round be x.
More radius , less round    (Indirect)
20: 14: :: 140 : x ⇒ 20x = (14*140 ) ⇒ x = (14 * 140/20 = 98.
Required number of round = 98.

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 - 25 men can reap a filed in 20 days . When should 15 men leave the work if the whole filed is to be reaped in 74/2 days after they leave the work?

Answer : C

Explanation

Let 25 men work for x days.
Work done = x/20 , Remaining work = (1- x/20).
25 men 1 days  work = 1/20.
1 men 1 days work = (1/20 * 1/25 ) = 1/500.
10  men 1 days work = (1/500 * 10 ) = 1/50.
10 men 75/2 days work = ( 1/50 * 75/2) = 75/100 = 3/4.
∴ (1 - x/20 ) = 3/4 ⇒ x/20 = 1/4 ⇒ x= (20 1/4 )= 5.
Hence , 15 men leave after 5 days.

Q 5 - If 9 men working hours 15/2 hours a day can finish a work in 20 days , then how many days will be taken by 12 men , working 6 hours a day to finish the work . It is given that 2 men of latter type work as much as 3 men of former type?

Answer : C

Explanation

2 men of latter type = 3 men of former tyes.
12 men of latter type = (3/2 *12) = 18 men of former tyes.
Let the required number of days be x.
More men , less days        (Indirect)
Men      18 : 9
:: 20 : x 
Working hrs  6 : 15 /2 
∴  18 *6 *x = 9 * 15/2 * 20 ⇒ x= 9 * 150/18 * 6 = 25/2 = 25/2 days.

Q 6 - A garrison of 500 men had provisions for 27 days. After 3 days ,a reinforcement of 300 men arrived. The remaining food will now last for how many days

Answer : A

Explanation

500 men had provisions for (27-3) = 24 days . Let the food for 800 men last for x days.
More men , less days         (Indirect)
800: 500 :: 24 : x ⇒ 800x = (500 * 24 ) ⇒ x = (500 * 24)/800 = 15 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 contractor undertook to do a certain piece of work in 9 days. He employed certain number of labourers. But , 6 of them being absent from the very first day ,the rest could finish the work in 15 days. The number of men originally employed were?

Answer : B

Explanation

let there be x men at the beginning.
Less men , more days     (indirect)
15:9 :: x : (x-6)⇒ 15 (x-6) = 9x ⇒ 6x = 90 ⇒x=15 men.

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