Question 1

20 persons completed 1/3rd of the work in 12 days. How many more person are required to finish the rest work in next 12 days?

Accepted Answer

Work done = 1/3 Remaining work = 2/3 So for double work in same days we need double number of people i.e. 40. So, 20 men will be increased.

Question 2

A and B can together do a piece of work in 15 days. B alone can do it 20 days. In how many days can A alone do it?

Accepted Answer

A's 1 day's work = (1/15 - 1/20) = 1/60 ∴ A alone can finish it in 60 days.

Question 3

A and B can do a piece of work in 6 days and A alone can do it in 9 days. The time taken by B alone to do the same work is?

Accepted Answer

B's one day's work = (1/6 - 1/9) = 1/18 ∴ B alone can finish it in 18 days.

Question 4

A and B can do a piece of work in 18 days, B and C in 24 days, A and C in 36 days. In what time can they do it all working together?

Accepted Answer

(A + B)'s 1 day's work = 1/18 (B + C)'s 1 day's work = 1/24 (A + C)'s 1 day's work = 1/36 Adding 2 (A + B + C)'s 1 day's work = (1/18 + 1/24 + 1/36) = 1/8 ∴ (A + B + C)'s day's work = 1/16 Hence, all working together can finish it in 16 days.

Question 5

A and B can do a piece of work in 12 days. B and C in 15 days. C and A in 20 days. A alone can do the work in?

Accepted Answer

∵ [(A + B) + (B + C) + (C + A)]'s 1 day's work = (1/12 + 1/15 + 1/20) = 1/5 ⇒ 2(A + B + C)'s 1 days work = 1/5 ⇒ (A + B + C)'s 1 day's work = 1/10 &rArr A's 1 day's work = (1/10 - 1/15) = 1/30 ∴ A alone can finish it in 30 days.

Question 6

A can do a piece of work in 30 days while B can do it in 40 days. In how many days can A and B working together do it?

Accepted Answer

(A + B)'s 1 day's work = (1/30 + 1/40) = 7/120 ∴ Time taken by both to finish the work = 120/7days = 171/7 days

Question 7

A can do (1/3) of a work in 5 days and B can do (2/5) of the work in 10 days. In how many days both A and B together can do the work?

Accepted Answer

∵ 1/3 of work is done by A in 5 days. ∴ Whole work will be done by A in 15 days. ∵ 2/3 of work is done by B in 10 days. Whole work will be done by B in 10 x (5/2) i.e., 25days ∴ (A + B)'s 1 day's work = (1/15 + 1/25) = 8/75 So, both together can finish it in 75/8 days, i.e., 93/8days.

Question 8

A can do a piece of work in 20 days which B can do in 12 days. B worked at it for 9 days. A can finish the remaining work in?

Accepted Answer

B's 9 day's work = 9 x (1/12) = 3/4 Remaining work = (1 - 3/4) = 1/4 1/4 work is done by A in = 20 x (1/4) = 5 days.

Question 9

A and B together can do a work in 8 days. If A alone can do it in 12 days, then in how many days can B alone do it?

Accepted Answer

Required time taken by B to complete the work = xy / x - y [Here x = 12 and y = 8] ⇒ required time = (12 x 8) / (12 - 8) = 96/4 = 24 days

Question 10

Rohan and Sunil separately can complete a work in 8 hours and 4 hours respectively. How much time will they take when working together?

Accepted Answer

Required time taken to complete the work by both together = x y / x + y (Here x = 8 and y = 4) ∴ Required time = (8 x 4)/(8 + 4) = 32/12 = 22/3 hours

Question 11

A can do a piece of work in 12 days. B is 60% more efficient than A. The number of days, it take B to do the same piece of work is?

Accepted Answer

A's 1 day's work = 1/12 B's 1 day's work = 1/12 + 60% of 1/12 = 1/12 x 160/100 = 2/15 ∴ B can do the work in 15/2 days = 71/2 days.

Question 12

A can finish a piece of work in 12 days while B can do it in 15 days. If both work at it together, what time will they take to do the work?

Accepted Answer

Efficiency of A = 100/12 = 8.33% Efficiency of B = 100/15 = 6.66% Combined efficiency of A and B = 8.33 + 6.66 = 15% Number of days taken by A and B, when worked together = 100/15 = 62/3 days

Question 13

A can do a piece of work in 14 days while B can do it in 21 days. In how many days, working together they will complete the whole work?

Accepted Answer

One day's work of A and B = 1/14 + 1/21 = 5/42 ∴ Required number of days = 42/5 = 8.4 days

Question 14

A can do a piece of work in 24 days. If B is 60% more efficient than A, then the number of days required by B to do the same piece of work is?

Accepted Answer

Efficiency of A = 4.16% Efficiency of B = 1.6 x 4.16 = 6.66% ∴ Number of days required by B = 100/6.66 = 15 days

Question 15

A is twice as good a workman as B and together they finish a piece of work in 14 days. In how many days can a alone finish the work?

Accepted Answer

One day's work of A and B = 1/x + 1/2x = 1/14 ∴ x = 21 Since A is twice efficient as B so A will take half of the day taken by B.

Question 16

Ajit is 3 times as efficient as Bablu, then the ratio of number of days required by each to work alone, completely?

Accepted Answer

Efficiency of Ajit : Bablu = 3 : 1 No. of days 1 : 3

Question 17

X is 4 times more efficient as Y , then the number of days taken by X and Y are in the ratio?

Accepted Answer

Efficiency (X : Y) = 5 : 1 No. of days (X : Y) = 1 : 5

Question 18

Sonu can do a piece of work in 20 days. He started the work and left after some days, when 25% work was done. After it Abhijeet joined and completed it working for 10 days. In how many days Sonu and Abhijeet can do the complete work, working togethe…

Accepted Answer

Efficiency of Sonu = (100/20) = 5% Rest work = 75% ∴ Efficiency of Abhijeet = 75/10 = 7.5% ∴ Combined efficiency of Sonu and Abhijeet = 7.5 + 5 = 12.5% ∴ Number of days required by Sonu and Abhijeet, to work togethere = 100/12.5 = 8days

Question 19

Three taps A, B and C together can fill a tank in 6 h. After working 2 h, C is closed and the tank was filled in 8 h more. Find the time in which C alone can fill the tank?

Accepted Answer

Work of (A + B + C) in 1 H = 1 / 6 Work done in 2 h = 2/6 = 1/3 Remaining part of the tank = 1 - 1/3 = 2/3 Time taken by A + B to fill this 2/3rd part of the tank = 8 h A and B together can fill tank in 12 h (i.e., 8 x 3/2). Now, we have A, B and C together filling the tank in 6 h and A and B together fill tank in 12 h. Work done by C alone in 1 h = 1/6 - 1/12 = 1/12 Hence, C alone can fill the tank in 12 h.

Question 20

Alen and Border can do a work individually in 21 and 42 days respectively. In how many days they can complete the work, working alternatively?

Accepted Answer

Alen's one day's work =1/21 Border's one day's work = 1/42 Alen and Border's two days work(working alternatively) = (1/21) + (1/42) = 1/14 So, Alen and Border do 1/14 work in 2 days So, they complete the work in 14 x 2 = 28 days.

Time and Work Questions