Question 1

A can do a piece of work in 10 days ,B can do it in 15 days. Working together they can finish the work in?

Accepted Answer

Efficiency of A = 10% Efficiency of B = 6.66% ∴ Required number of days = 100/16.66 = 6 days

Question 2

A can do a piece of work in 24 days, while B can do it in 30 days. With the help of C they can finish the whole work in 12 days.How much time is required for C to complete the work, alone?

Accepted Answer

Efficiency of A = 100/24 = 4.16% Efficiency of B = 100/30 = 3.33% Efficiency of (A+ B+C) =100/12 = 8.33% ∴ Efficiency of C = (8.33) - (4.16 + 3.33) = 0.83% ∴ Number of days required by C to complete the work alone = 100/0.83 = 100/(5/6) = 120 days (Note : 5/6 = 0.833)

Question 3

A is thrice efficient as B and C is twice as efficient as B. what is the ratio of number of days taken by A,B and C , when they work individually?

Accepted Answer

A : B : C Ratio of efficiency 3 : 1 : 2 Ratio of number of days { 1/3 : 1/1 : 1/2 } or 2 : 6 : 3 Hence, (a) is correct [ Time = 1/ Efficiency ]

Question 4

If A takes 4/5 days as B takes and working together they require 20/3 days to complete the whole work. What is the efficiency of B?

Accepted Answer

Efficiency of A + B = 100/(20/3) = 15% No. of days ( A:B ) = 4 : 5 Efficiency ( A:B ) = 5 : 4 ∴ Efficiency of B = (4/9) x 15 = 20/3 = 62/3%

Question 5

A is thrice as efficient as B. Working together they complete the work in 3 days. If B take 8 days more then A, What is the number of days taken by A to finish the while work, alone?

Accepted Answer

Efficiency of A + B = 33.33% = 100/3 Ratio of efficiency of A and B = 3 : 1 ∴ Efficiency of A = (3/4) x 33.33 = 25% ∴ Number of days taken by A = 100/25 = 4

Question 6

A and B can do a piece of work in 12 days B and C in 15 days C and A in 20 days. In how many days can C alone do it?

Accepted Answer

Efficiency of (A + B) = 8.33% Efficiency of (B + C) = 6.66% Efficiency of (C + A) = 5.00% ∴ Efficiency of A + B + C = (8.33 + 6.66 + 5) / 2 = 10% ∴ Efficiency of C = Efficiency of [(A + B + C) - (A + B) ] = (10 - 8.33) = 1.66% ∴ No. of days required by C alone = 100/1.66 = 60days

Question 7

A and B can do a piece of work in 8 days, B and C can do the same work in 12 days and A and C complete it in 8 days. In how many days A, B and C can complete the whole work,working together?

Accepted Answer

Efficiency of (A + B) = 12.5% Efficiency of (B + C) = 8.33% Efficiency of (C + A) = 12.5% ∴ Efficiency of [(A + B) + (B + C) + (C + A)] = 33.33% ∴ Efficiency of (A + B + C) = 16.66% ∴ No. of days Required by A, B and C together = 100/16.66 = 6 days

Question 8

A, B and C working in a garment manufacturing company can do the same assignment in 24, 6 and 12 days, respectively. Working together the assignment will be complete in how many days?

Accepted Answer

(A + B + C)' S 1 day's work = (1/24) + (1/6) + (1/12) = 7/24 ∴ (A + B + C) can do the entire work in = 24/7 = 33/7 days

Question 9

A women can weave a basket in 6 days. But with the help of her daughter, she can complete the work in 4 days. In what time can the daughter alone do the work?

Accepted Answer

Women's 1 day's work = 1/6 (Women + Daughter)'s 1 day's work = 1/4 ∴ Daughter's 1 day's work = 1/4 - 1/6 = 1/12 So, the daughter can do the work in 12 days.

Question 10

Working together P and Q can do a job is 6 days. Q and R can do the same job in 10 days while P and R can do it in 5 days. How long will it take, if all of them work together to complete the job?

Accepted Answer

(P + Q)'S 1 day's work = 1/6 (Q + R)'s 1 day's work = 1/10 (P + R)'s 1 day's work = 1/5 On adding, 2 (P + Q + R)'s 1 day's work = 1/6 + 1/10 + 1/5 = 7/15 ( P + Q + R)'s 1 day's work = 7/30 ∴ (P + Q + R)'s can do the entire work in = 30/7 = 42/7 days

Question 11

The efficiency of Romil is twice that of Sanjay and he can finish a work in 4 h less than the time taken by Sanjay. If both of them work together they can finish the same work in?

Accepted Answer

As the efficience of Romil is twice that of Sanjay, Romil, will take x h for completeion of the work, when Sanjay is taking 2x h. Given, 2x - x = 4 ⇒ x = 4 Hence, they take = 1/(1/4 + 1/8) = 8/3 h

Question 12

A man is paid ₹ 5 per h for regular working day and ₹ 8 per h overtime. A regular working day has 8 h and a regular week has 5 working days. If he earns ₹ 920 in 4 weeks, then what is the total number of hours that he worked assuming that he was pre…

Accepted Answer

Number of regular hours during 4 weeks = 8 x 5 x 4 = 160 Amount paid for regular working hours = 160 x 5 = ₹ 800 Balance left = (920 - 800) = ₹ 120 So, ₹ 120 is paid for his over time at ₹ 8 per h. ∴ Total number of overtime working hours = 120/8 = 15 h Total working hours = (160 + 15) = 175 h

Question 13

Pipes A and B can fill a tank in 20 h and 30 h, respectively and pipe C can empty the full tank in 40 h. If all the pipes are opened together, how much time will be needed to make the tank full?

Accepted Answer

Net part filed in 1 h = (1/20 + 1/30 - 1/40) = 7/120 Hence, the tank will be full in 120/7 = 171/7 h

Question 14

A man, a women and a boy can do a job in 3, 4 and 12 days , respectively. How many boys must assist one man and one women to complete the job in one and a half days?

Accepted Answer

Portion of work completed by one man in 11/2 days. i.e., 3/2 days = 3/(2 x 3) = 1/2 Portion of work completed by one women in 11/2 days. i.e., 3/2 days = 3/(2 x 4) = 3/8 ∴ Portion of work completed by boys = 1 - (1/2 + 3/8) = 1/8 Now, portion of work completed by each boy in 3/2 days = 3/(2 x 12) = 1/8 Hence, only one boys would be required.

Question 15

A leak in the bottom of a tank can empty the full tank in 6 h. An inlet pipe fills water at the rate of 4 L in a min. When the tank is full, the inlet is opened and due to the leak the tank is empty in 8 h. Find the capacity of the tank?

Accepted Answer

Efficiency of the leak = 1/6 Combined efficiency of leak and inlet pipe So, efficiency of inlet pipe = 1/6 - 1/8 = (4 - 3)/24 = 1/24 Inlet pipe can fill the tank in 24 h, at rate of 4 L/min. ∴ Capacity = 24 x 60 x 4 = 5760 L

Question 16

A and B can do a piece of work in 12 days, B and C can do it in 15 days and C and A can do the same work in 20 days. Find the number of days in which A alone can do the same job?

Accepted Answer

Work done by A and B in one day = 1/12 Work done by B and C in one day = 1/15 Work done by C and A is one day = 1/20 On adding all these, 2(A + B + C)'s work of one day = 1/12 + 1/15 +1/20 = 1/5 ⇒ (A + B + C)'s one day work = 1/10 ∴ A' s one day work = (A + B + C)'s one day work - (B + C )'s one day work ⇒ A's one day work 1/10 - 1/15 = 1/30 Hence, A can do this work in 30 days.

Question 17

Two friend A and B working together completed a work in 26 days. Their skills of doing the work are in the ratio 8 : 5. How many days will B take, if engaged alone?

Accepted Answer

Skill ratio of A and B = 8 : 5 So, the time taken by A and B 5W and 8W, respectively. According to the question, 1/8W + 1/5W = 1/26 ∴ W = (13 x 26)/40 Now, time taken by B is 8W = 8 x 13 x 26/40 = 673/5 days.

Question 18

A and B together can complete a piece of work in 35 days while A alone can complete the same work in 60 days. In how many days, B alone will be able to complete the same work?

Accepted Answer

In this question, A and B did the work for 35 days to complete it. A can complete the work in 60 days. So, A did/A can + B did/B can = 1 ⇒ 35/60 + 35/x = 1 ⇒ x = 84 days

Question 19

A and B can do a piece of work in 72 days, B and C can do it in 120 days, A and C can do it in 90 days. In what time can A alone do it?

Accepted Answer

Combined efficiency of A and B = 1/72 ....(i) Combined efficiency of B and C = 1/120 ....(ii) Combined efficiency of A and C = 1/90 ....(iii) On adding Eqs. (i), (ii) and (iii), we get 2(A + B + C) = 1/72 + 1/120 + 1/90 = (5 + 3 + 4)/360 = 12 / 360 = 1 / 30 ⇒ A + B + C = 1/60 .....(iv) i.e Combined efficiency is 1/60 or we can say together A, B and C can complete the work in 60 days. On subtracting Eq. (ii)from Eq. (iv), we get Efficiency of A = Combined efficiency of A, B and C - Combined efficiency of B and C = 1/60 - 1/120 = 1/120 Hence, A alone can do it in 120 days

Question 20

Ram finishes a work in 7 days. Rahim finish the same job in 8 days and Robert in 6 days. They take turns to finish the work. Ram worked on the first day, Rahim on the second day and Robert on the third and then again Ram and so on. Who was working o…

Accepted Answer

Three day work or Ram, Rahim and Robert = 1/7 + 1/8 + 1/6 = (24 + 21 + 28)/168 = 73/168 Their six days work = (2 x 73)/168 = 146/168 = 73/84 Now, its Ram's turn to work on seventh day. ∴ 73/84 + 1/7 = 73 + 12/84 = 85/84 > 1 So, Ram will finish the work before the end of day. Hence, Ram is working for the last day.

Time and Work Questions