Question 1

Two pipes A and B can each fill a tank in 40 and 60 min, respectively. There is an outlet C. If all the 3 pipes are opened up, the tank will be filled in 30 min. How much time will it take for C alone to empty the full tank?

Accepted Answer

Work done by C in one min = (1/40 + 1/60) - 1/30 = 1/120 Hence, C can empty the tank in 120 min or 2 h.

Question 2

A conveyer belt delivers baggage at the rate of 3 tonne in 5 min and a second conveyer belt delivers baggage at the rate of 1 tonne in 2 min. How much time will it take to get 33 tonne of baggage using both conveyer belts?

Accepted Answer

The weight of baggage deliver in 1 min by 1st belt = 3/5 tonne The weight of baggage deliver in 1 min by 2nd belt = 1/2 tonne The weight of baggage deliver in 1 min by both belt = 3/5 + 1/2 = 11/10 tonne So, the two belts delivers 1 tonne in 10/11 min. Hence, required time to deliver 33 tonne = (10/11) x 33 = 30 min

Question 3

Rohit, Harsh and Sanjeev are three typists, who working simultaneously, can type 216 pages in four hours . In one hour, Sanjeev can type as many pages more than Harsh as Harsh can type more than Rohit. During a period of five hours, Sanjeev can type…

Accepted Answer

Let Rohit, Harsh and Sanjeev can type x, y and z pages respectively in 1 h. Therefore, they together can type 4(x + y + z) pages in 4 h ∴ 4(x + y + z) = 216 ⇒ x + y + z = 54 .....(i) Also, z - y = y - x i.e., 2y = x + z ......(ii) From Eqs. (i) and (ii), we get 3y = 54 ⇒ y = 18 From Eq. (ii), x + z = 36 ....(iv) From Eqs. (iii) and (iv), we get x = 15 and z = 21

Question 4

A and B together can do a piece of work in 12 days which B and C together can do in 16 days. After A has been working at it for 5 days and B for 7 days, C takes up and finishes it alone in 13 days. In how many days, C alone can do the work?

Accepted Answer

(A + B)'s one day work = 1/12 (B + C)'s one day work = 1/16 Now, from the question, A's 5 days work + B's 7 days work + C's 13 days work = 1 ⇒ A's 5 days work + B's 5 days work + B's 2 days work + C's 2 days work + C's 11 days work = 1 (A + B)'s 5 days work + (B + C)'s 2 days work + C's 11 days work = 1 ⇒ 5/12 + 2/16 + C's 11 days work = 1 ⇒ C's 11 days work = 1 - (5/12 + 2/16) = 11/24 ⇒ C's 1 day work = (11/24) x 11 = 1/24 Hence, C can do this work in 24 days.

Question 5

A and B can complete a piece of work in 12 days while B and C in 15 days. A did the work for 3 days, B for 8 days and C for 10 days to complete the work. In how many days C alone can complete the work?

Accepted Answer

Fraction of work complete by (A and B) + Fraction of work complete by (B and C) + Fraction of work completed by C = 1 As B did the work for 8 days we can say B did the work for 3 days with A and B did the work for 5 days with C. So, A and B together did the work for 3 days, B and C together did the work for 5 days, C alone did the work for 5 days. ∴ 3/12 + 5/15 + 5/x = 1 or 5/x = 5/12 i.e., x = 12 or C alone can complete the work in 12 days

Question 6

A supplies 20 men who work for 8 h per days for 6 days. B supplies 15 men working at 9 h per day for 7 day and C supplies 10 men working 6 h per day for 8 days to do a certain lob. If ₹ 636 is paid for all the labour, what is C's share?

Accepted Answer

Total man hours work done by men supplied by A, B and C = (20 x 8 x 6), (15 x 9 x 7), (10 x 6 x 8) and the wages must be in the ratio of the work done. So, ₹ 636 has to divided among A, B and C in the ratio (20 x 8 x 6) : (15 x 9 x 7) : (10 x 6 x 8) = 64 : 63 : 32 ∴ C's share = (32/159) x 636 = ₹ 128

Question 7

A and B can do a piece of work in 45 days and 40 days, respectively. They began to do the work together but A left after some days and then B completed the remaining work in 23 days. The number of days after which A left the work, is?

Accepted Answer

By the fundamental of work and time, x/45 + (x + 23)/40 = 1 ⇒ x = 9 days

Question 8

50 men or 80 women can finish a job in 50 days. A contractor deploys 40 men and 48 women for this work but after every duration of 10 days, 5 men and 8 women are removed till the work is completed. The work is completed in?

Accepted Answer

Since, 50 men can do a job in 50 days. So, work done by 1 man in a day = 1/(50 x 50) Also, 80 women can do the job in 50 days. So, work done by 1 women in 1 day = 1/(50 x 80) Now, work done by 40 men and 48 women in first 10 days = (40 x 10)/(50 x 50) + (48 x 10)/(50 x 80) = 4/25 + 3/25 = 7/25 Now, 5 men and 8 women are removed after 10 days, So work done by 35 men and 40 women in 10 days = (35 x 10)/(50 x 50) + (40 x 10)/(50 x 80) = 7/50 + 1/10 = (7 + 5)/50 = 6/25 Again, 5 men and 8 women are removed after 10 days, So work done by 30 men and 32 women in 10 days = (30 x 10)/(50 x 50) + (32 x 10)/(50 x 80) = 5/25 Now, after every 10 days as the number of men and women decrease, work done also decreased by 1/25th past. So, work done after every 10 days upto 50 days = 7/25 + 6/25 + 5/25 + 4/25 + 3/25 = 25/25 = 1 So, it will take 50 days for them to complete the work.

Question 9

A can do a piece of work in 10 days, B in 15 days. They work together for 5 days, the rest of the work is finished by C in two more days. If they get Rs 3000 as wages for the whole work, what are the daily wages of A, B and C respectively (in Rs )?

Accepted Answer

A's 5 day work = 50% B's 5 day work = 33.33% C's 2 day work = 16.66% [100 - (50 + 33.33)] Ratio of contribution of work of A , B and C = 50 : 33.33 : 16.66 = 3 : 2 : 1 A's total share = Rs. 1500 B's total share = Rs. 1000 C's total share = Rs. 500 A's one day's earning = Rs. 300 B's one day's earning = Rs. 200 and C's one day's earning = Rs. 250

Question 10

Efficiency of Asha is 25% more then Usha and Usha takes 25 days to complete a piece of work. Asha started a work alone and then usha joined her 5 days before actual completion of the work. For how many days Asha worked alone?

Accepted Answer

Efficiency (Asha : Usha) = 5 : 4 Number of days(Asha : Usha) = 4x : 5x = 4x : 25 ∴ Number of days required by Asha to finish the work alone = 4x = 4 x 5 = 20. Now, since Asha and Usha did work together for last 5 days = 5 x 9 = 45% (since efficiency of Asha = 5% and Usha's efficiency = 4%) It means Asha completed 55% work alone. ∴ No. of days taken by Asha to complete 55% work = 55/5 = 11days

Question 11

Krishna can do a work in 10 days while Mohan can do the same work in 20 days. They started work together. After 3 days Krishna left the work and Mohan completed it. For how many days Mohan worked alone more than the No. of days required when both wo…

Accepted Answer

Krishna's efficiency = 10% Mohan's efficiency = 5% Work done by Krishana and mohan together in 3 days = 15 x 3 = 45% Now, number of days in which B completed rest (55%) work alone = 55/5 = 11 Total No. of days in which B worked = 3 + 11 = 14 Now No. of days required by B, when A and B both worked together = 100/15 = 62/3 ∴ Required difference in No. of days = (11) - (62/3) = 13/3 = 4 1/3 days

Question 12

Kareena can do a piece of work in 9 days and Krishna can do the same work in 18 days. They started the work. After 3 days Shahid joined them, who can complete alone the same whole work in 3 days. What is the total No. of days in which they had compl…

Accepted Answer

Efficiency of Kareena and Krishna = 11.11 + 5.55 = 16.66% Work done in 3 days = 3 x 16.66 = 50% Rest work done by Kareena, Krishna and Shahid = 50/50 = 1 day (Since efficiency of Shahid = 33%) Thus in ( 3 + 1) days they have completed the work = 4 days.

Question 13

kavita, babita and samita started a work. 5 days later Samita left the work and Babita left the work after working 8 days. In how many more days Kavita would have completed the rest work if they take 20, 60 and 30 days individually to finish a work?

Accepted Answer

Efficiency of Kavita = 5% Efficiency of Babita = 1.66% Efficiency of Samita = 3.33% Work done in 5 days by K + B + S = 5 x 10 = 50% Work done in 3 days by K + B = 3 x 6.66 = 20% Remaning work (30%) done by Kavita alone = 30/5 = 6 days

Question 14

In a school, MID-Day meal food is sufficient for 250 students for 33 days. if each students is given 125 g meals. 80 more students joined the school. If same amount of meal is given to each student, then the food will last for

Accepted Answer

M1 = 250, D 1 = 33 days per day meal W1 = W2 = 125 g M2 = (250 + 80) =330 and D2=? According to the formula M1D1W2 = M2D2W1 250 x 33 x 125 = 330 x D2x 125 ⇒ D2 = (250 x 33)/330 ∴ D2 = 25 days

Question 15

A certain number of men can do a piece of work in 80 days. If there were 10 men less, it could be finished in 20 days more. How many men are there in the starting?

Accepted Answer

Let the original number of men = N Time taken by N = 80 days Now, (N - 10) men can finish the work in the (80 + 20) = 100 days Here, M1 = N, M2 = (N - 10), D1 = 80 and D2 = 100 According to the formula. M1D1 = M2D2 ⇒ N x 80 = 100 x (N - 10) ⇒ 8N = 10N - 100 ⇒ 10N - 8N = 100 ⇒ N = 50

Question 16

A can do a piece of work in 8 days, B can do it in 10 days and C can do it in 20 days. In how many days can A, B and C together complete the work?

Accepted Answer

A's 1 days 's work = 1/8 B ' s 1 days ' s = 1/10 C ' s day 's work = 1/20 (A + B + C)'s 1 days 's work = 1/8 + 1/10 + 1/20 = (5 + 4 + 2)/40 = 11/40 ∴ (A + B + C ) can finish the work in 40/11 days or 3 7/11 days.

Question 17

15 men would finish a piece of work in 210 days. But at the end of every 10 days. 15 additional men are employed. In how many days will it be finished?

Accepted Answer

10 day's work by 15 men = 10/210 = 1/21 At the end of every 10 days 15 additional men are employed i.e., for the next 10 days we have 15 + 15 = 30 men ∴ Next 10 day's work by 30 men = 2/21 Hence in 20 days only (1/21 + 2/21) = 3/21 work is completed To complete the whole work we have to reach the value of (21/21) work. Now, (1/21) + (2/21) + (3/21) + ......... (6/21) = 21/21 = 1 Hence total time to complete the whole wok 10 + 10 + 10 + 10 + 10 + 10 = 60 days

Question 18

Ramesh can finish a job in 20 days. He worked for 10 days alone and completed the remaining job working with Dinesh, in 2 days. How many days would both Dinesh and Ramesh together can complete the whole work?

Accepted Answer

Ramesh alone finish 1/2of the work in 10 days. Remaining 1/2 of the job was finished by Ramesh and Dinesh together in 2 days. Therefore, they both together can finish the complete job in 4 days.

Question 19

A and B can together finish a work in 30 days. They worked for it for 20 days and then B left. the remaining work was done by A alone in 20 more days. A alone can finish the work in?

Accepted Answer

(A + B)'s 20 day's work = (20 x 1/30) = 2/3 Remaining work = (1 - 2/3) = 1/3 1/3 work is done by A in 20 days Whole work can be done by A in (3 x 20) days = 60 days.

Question 20

Two workers A and B working together completed a job in 5 days. If A worked twice as efficiently as he actually did and B worked 1 / 3 as efficiently as he actually did the work, then they would have completed the work in 3 days. Find the time for A…

Accepted Answer

Efficiency is proportional to work done per day. Work done per day N number of days = Amount of work done. Considering efficience of A and B initially as 1. Let A alone can do the work in M days and B alone can do the same work in N days. Then, 5/M + 5/N = Total work done = 1 Since efficiency of A and B are 2 and 1/3 respectively ⇒ 6/M + 1/N = 1 ....(i) and 1/M + 1/N = 5 .....(ii) Now, subtracting equation (ii) from equation (i), we have M = 25/4 = 61/4 days.

Time and Work Questions