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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 garrison of 500 men had provisions for 24 days . However a reinforcement of 300 men arrived . The food will now last for

Answer : D

Explanation

Let the required number of days be x.
More men , less days      (indirect)
800 : 500  :: 24 : x ⇒ 800x = (500 * 24 ) ⇒ x = (500 * 24 ) / 800  = 15.
∴ The food will now last for 15 days.

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 - 10 women can complete a piece of work in 8 days and 10 children take 12 days to complete it. How many days will 6 women and 3 children together take to complete the work?

Answer : C

Explanation

1 women can complete the work in ( 10 * 8) = 80 days.
1 child can complete the work in ( 10 * 12) = 120 days.
1 women 1 days work = 1/80, 1 child 1 days work = 1/120.
( 6women  + 3 children) 1 days work = ( 6 * 1/80 + 3 * 1/120) = ( 3 /40 + 1/40 ) = 4/40=1/10.
Required time 10 days.

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 - 40 men take 8 days to ears Rs 2000. How many men will earn Rs 200 in 2 days?

Answer : A

Explanation

Let  the required number of  men  b  x.
Less  earning , less men     (Direct)
Less days , less men      (Direct)
Earning     2000  : 200
:: 40 : x
Days       8 :  2
∴ (2000 * 8 * x ) = (200 * 2 * 40 ) ⇒ x = 200* 2 * 40 / 2000 * 8  = 1 .
Required number of men = 1.

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 - 400 persons working 9 hours per day complete 1/4 th of the work in 10 days . The number of additional persons , working 8 hours per day required to complete the remaining work in 20 days , is:

Answer : D

Explanation

Let the number of additional men be x .
Less hrs per days, more men       ( Indirect)
More days , less men              ( Indirect)
More work, more men         ( Direct)
Her/ days   8:9
Days    20 : 10
:: 400 : ( 400 + x ) 
Work 1/4 : 3/4
∴ 8 * 20 * 1/4 * ( 400 + x ) = 9 * 10 * 3/4 * 400
⇒ ( 400 + x ) = 9 * 10 * 3 * 400/ 8 * 20  = 675.
Number of  additional men = 675.

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 - 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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