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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 - If 4/5th of a cistern is filled in 1 minute, how much more time will be required to fill the rest of it?
Answer : B
Explanation
Let the required time be x seconds. Part filled = 4/5, Remaining part = (1- 4/5 ) = 1/5. Less part to be filled , less is the time taken (direct) 4/5 :1/5 :: 60 : x ⇒ 4/5 * x = (1/5 * 60 ) = 12 ⇒ x= (12 * 5/4 ) = 15. Required time = 15 seconds.
Q 2 - 16 men can reap a field in 30 days . In how many days will 20 men reap the field?
Answer : B
Explanation
Let the required number of days be x. More men , less days (Indirect) 20 : 16 :: 30 : x⇒ 20x = (16 *30 ) ⇒ x = (16*30)/20 =24days.
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 - A does half as much work as B in one- sixth of time. If together they take 10 days to complete the work, how much time shall B alone take to do it ?
Answer : B
Explanation
Suppose B takes x days to finish the work . Then , A takes x/6 days to finish half the work . ∴ A takes 2x / 6 = x/3 days to finish the work. 1/x + 3/x = 1/10 ⇒ 4/x = 1/10 ⇒ x= 40. Hence , B along takes 40 days to finish the work.
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 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 3 persons weave 336 shawls in 14 days , how many shawls will 8 persons weave in 5 days?
Answer : D
Explanation
Let the required number of shawls be x. More persons, more shawls (Direct) Less days, less shawls (Indirect) Persons 3:8 :: 336 : x Days 14: 5 ∴ ( 3 * 14 * x ) = ( 8 * 5 * 336) ⇒ x = 8 * 5 * 336/ 3 * 14 = 320.
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.