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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 - The Qutab minar casts a shadow 150m long at the same time when the vikes minar casts a shadow 120m long on the ground . If the height of the Vikes minar is 80m, what is the height of the Qutab Minar?
Answer : A
Explanation
Let the height of the Qutab Minar be x metres. Longer is the shadow , longer is the object (Direct) 120 : 150 :: 80 : x ⇒ 120 * x = (150 *80)⇒ x= (150 *80)/120=100m. Height of Qutab Miinar = 100m.
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 and 12 children can do a piece of work in 9 days . A child takes double the time to do a work than the men. In how many days 12 men can complete the work?
Answer : A
Explanation
2 children = 1 men ⇒ (8 men + 12 children ) = 14 men. Let the required number of days be x. Less men , more day (Indirect ) 12 : 14:: 9 : x ⇒ 12x = ( 14 * 90 ⇒ ( 14* 9 ) /12 = 21 /2 = 21/2 days.
Q 5 - In a barrack of soldiers there was stock of food for 190 days for 4000 soldiers.After 30 days , 800 soldiers left the barrack. For how many days shall the left over Food last for the remaining soldiers?
Answer : B
Explanation
Remaining food was sufficient for 4000 soldiers for 160 days. Remaining soldiers = ( 4000- 800) = 3200. Let the required number of days be x . Less soldiers, more days (Indirect) 3200 : 4000 :: 160 : x⇒ 3200 x = (4000 * 160 ) ⇒ x = (4000 * 160)/3200 = 200 days.
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 - 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 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 - If x men working x hours per day can do x unit of work in x days , then y men working y hours per day would be able to do how much work in y days?
Answer : D
Explanation
More men , more work (Direct) More working hrs , more work (Direct) More days , more work (Direct) Let the required work be z units. Then, Men x:y working hrs x:y :: x:z days x:y ∴ x*x*x*z = y * y* y* x ⇒ z= y3 / x2 units.