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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 - 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 - 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 - A garrison of 3300 men had provisions for 32 days , when given at the rate of 850 gm per head . At the end of 7 days , a reinforcement arrived and it was found that the provisions would last 17 days more , when given at the rate of 825 gm per head . What was the strength of the reinforcement?
Answer : C
Explanation
Let the required strength of reinforcement be x. 3300 men had provisions for (32-7 ) = 25 days. Less food per head , more persons (Indirect) Less days , more persons (Indirect) Food per days 825 : 850 :: 3300 : (3300 x ) Days 17 : 25 ∴ 825 * 17 * (3300 + x ) = 850 * 25 * 3300 ⇒ ( 3300 + x ) = 850 * 25 * 3300/825 * 17 = 5000 ⇒ x = ( 5000 - 3300) = 1700 men.
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 - 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 the number of additional men 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) = 32 ⇒ x=12. Required number of days = 12.