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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 worker makes a toy every 2/3 hour. If he works for 15/2 hours, then how many toys will he makes?

Answer : A

Explanation

Let the required number of toys be x.
More time , more toys made   (Direct)
2/3 : 15/2 :: 1:x ⇒ 2/3 * x = 15/2 *1 ⇒ x= (15/2 *3/2 ) = 45 /4 = 45/4.
Required number  of toys = 45/4.

Q 2 - A tree 6m tall casts a 4m long shadow. At the same times, a flagpole casts a 50 m long shadow. How long is the flagpole?

Answer : B

Explanation

Let the length of the flagpole be x metres.
Longer is the shadow, longer is the object (Direct)
4: 50 :: 6:x ⇒ 4x = (50 * 6 ) ⇒ x= (50*6 )/4 =75m.
Length of flagpole = 75m.

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 - 8 men can finish a piece of work in 40 days . If 2 more men join with them , then the work will be completed in?

Answer : B

Explanation

Let  10 men finish it in x days.
More men, less days     (Indirect)
10 : 8 :: 40 : x ⇒ 10x = (8 * 40 ) ⇒ x = (8*40) /10 = 32 days.

Q 5 - If a job takes 12 workers 4 hours to complete, how long should it take 15 workers to complete the job?

Answer : C

Explanation

Let the required number of  hours b x.
More working , less  hours             (Indirect)
15 : 12 :: 4 : x = > 15 x = ( 12 * 4 ) ⇒ x= (12 * 4 ) /15 = 16 / 5 hrs = 3hrs 12 min.

Q 6 - A contractor undertakes to build a wall in 50 days. He employs 50 people for the same . However, after 25 days , he finds that only 40 % of the work is complete , How many more men need to be employed to complete the work in time?

Answer : B

Explanation

Work done = 40/100 = 2/5 , Remaining work = ( 1 - 2/5 ) = 3/5.
2/5 work is done in 25 days by 50 people.
3/5 work will be done in 25 days by (50 * 5/ 2 * 3/5) people = 75 people.
Required number of people = ( 75 ? 50 )  = 25.

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 18 binders bind 9000 books in 10 days , how many binders will be required to bind 6600 books in 12 days?

Answer : D

Explanation

Let the required number of binders be x.
Less books, less binders   (direct)
More days, less binders    (Indirect)
Books 9000:6600
Days   12:10                   :: 18 : x
∴ (9000* 12*x) = (6600 * 10 *18)⇒ x= 6600 * 10 *18/9000 *12 = 11

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.

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