Question 1

A can do a piece of work in 30 days. He works at it for 6 days and then B finishes it in 18 days. In what time can A and B together it ?

Accepted Answer

Let 'B' alone can do the work in 'x' days 6/30 + 18/x = 1 => x = 22.5 1/30 + 1/22.5 = 7/90 => 90/7 = 12 6/7 days

Question 2

Amit can do a piece of work in 45 days, but Bharath can do the same work in 5 days less, than Amit, when working alone. Amit and Bharath both started the work together but Bharath left after some days and Amit finished the remaining work in 56 days …

Accepted Answer

A m i t B h a r a t N o . o f D a y s 45 40 E f f i c i e n c y 2 . 22 P e r c e n t ( = 1 45 ) 2 . 5 P e r c e n t ( = 1 40 ) Amit did the work in 56 days = 56 × 1 45 × 2 = 28 45 Therefore, Rest work 17/45 was done by Amit and Bharath = 17 45 17 360 = 8 days ( since Amit and Bharath do the work in one day = 1 45 + 1 40 = 17 360 )

Question 3

P alone can do a piece of work in 24 days. The time taken by P to complete one-third of work is equal to time taken by Q to complete half of the work. How many days are required to complete by P and Q working together ?

Accepted Answer

Let the total work be 'W' As per the given information, P can complete the work 'W' in 24 days. => one day work of P = W/24 And also given that, The time taken by P to complete one-third of work is equal to time taken by Q to complete half of the work => PW/3 = QW/2 => P's 1 day = W/24 ? = W/3 => ? = 24W/3W = 8 => QW/2 = 8 days => Q alone can complete the work W in 16 days => P + Q can complete the work in 1/24 + 1/16 = 5/48 => 48/5 days = 9 3/5 days.

Question 4

If 6 men and 8 boys can do a piece of work in 10 days while 26 men and 48 boys can do the same in 2 days what is time taken by 15 men and 20 boys?

Accepted Answer

Given that 6 men and 8 boys can do a piece of work in 10 days 26 men and 48 boys can do the same in 2 days As the work done is equal, 10(6M + 8B) = 2(26M + 48B) 60M + 80B = 52M + 96B => M = 2B => B = M/2 ……(1) Now Put (1) in 15M + 20B => 15M + 10M = 25M Now, 6M + 8B in 10 days => (6M + 4M) 10 = 100M Then D(25M) = 100M => D = 4 days.

Question 5

P and Q can complete a job in 24 days working together. P alone can complete it in 32 days. Both of them worked together for 8 days and then P left. The number of days Q will take to complete the remaining work is ?

Accepted Answer

(P+Q)'s 1 day work = 1/24 P's 1 day work = 1/32 => Q's 1 day work = 1/24 - 1/32 = 1/96 Work done by (P+Q) in 8 days = 8/24 = 1/3 Remainining work = 1 - 1/3 = 2/3 Time taken by Q to complete the remaining work = 2/3 x 96 = 64 days.

Question 6

After working for 8 days, Arun finds that only 13 rd of the work has been done. He employs Akhil who is 60% as efficient as Arun. How many days more would Akhil take to complete the work?

Accepted Answer

Arun has completed 1 3 rd of the work in 8 days Then he can complete the total work in 1 3 ---- 8 1 ---- ? = 24 days But given Akhil is only 60% as efficient as Arun Akhil = 1 24 × 60 100 = 1 40 Akhil can complete the total work in 40 days Now, remaining 2/3rd of work can be completed in 1 ------ 40 2 3 ------ ? = 26.66 days.

Question 7

If 10 men take 15 days to complete a work. In how many days will 37 men complete the work?

Accepted Answer

Given 10 men take 15 days to complete a work => Total mandays = 15 x 10 = 150 Let the work be 150 mandays. => Now 37 men can do 150 mandays in 150/37 =~ 4 days

Question 8

6 men can complete a piece of work in 12 days. 8 women can complete the same piece of work in 18 days whereas 18 children can complete the piece of work in 10 days. 4 men, 12 women and 20 children work together for 2 days. If only men were to comple…

Accepted Answer

Given 4men, 12 women and 20 children work for 2 days. Workdone for 2 days by 4men, 12 women and 20 children = 4 x 2 6 x 12 + 12 x 2 8 x 18 + 20 x 2 18 x 10 = 1 2 Therefore, remaining work = 1 - 1 2 = 1 2 To complete the same work by only men in 1 day, We know that M1 x D1 = M2 x D2 Here M1 = 6 , D1 = 12 and M2 = M , D2 = 1 12 x 6 = M x 1 => M = 12 x 6 = 72 => But the remaining work = 1/2 Men required => 1/2 x 72 = 36 Only men required to Complete the remaining work in 1 day = 36.

Question 9

4 men and 6 women can complete a work in 8 days, while 3 men and 7 women can complete it in 10 days. In how many days will 10 women complete it ?

Accepted Answer

Let 1 man's 1 day work = x and 1 woman's 1 day work = y. Then, 4x + 6y = 1/8 and 3x + 7y = 1/10 Solving these two equations, we get: x = 11/400 and y = 1/400 10 woman's 1 day work = (1/400 x 10) = 1/40. Hence, 10 women will complete the work in 40 days.

Question 10

12 men complete a work in 9 days. After they have worked for 6 days, 4 more men join them. How many days will they take to complete the remaining work ?

Accepted Answer

1 man's 1 day work = 1/108 12 men's 6 day's work = 1/9 x 6 = 2/3 Remaining work = 1 - 2/3 = 1/3 16 men's 1 day work = 1/108 x 16 = 4/27 4/27 work is done by them in 1 day. 1/3 work is done by them in 27/4 x 1/3 = 9/4 days.

Question 11

M can complete a piece of work in 10 days. N is 33.33% less efficient than M. calculate the number of days required to both to complete the work?

Accepted Answer

M = 10 days The ratio of efficiency of M & N are 3 : 2 Hence, the time rquired for N alone = 15 days => Required time taken t=by both to complete the work = M x N / M + N = 10 x 15/ 10 + 15 = 150/25 = 6 days.

Question 12

Four pipes P,Q, R and S can fill a cistern in 20,25, 40 and 50 hours respectively.The first pipe P was opened at 6:00 am, Q at 8:00 am, R at 9:00 am and S at 10:00 am. when will the Cistern be full?

Accepted Answer

Efficiency of P= 100/20= 5% per hour Efficiency of Q= 100/25= 4% per hour Efficiency of R= 100/40= 2.5% per hour Efficiency of S=100/50= 2% per hour Cistern filled till 10 am by P, Q and R Till 10 . 00 am Pipe P filled 20 % Till 10 . 00 am Pipe Q filled 8 % Till 10 . 00 am Pipe R filled 2 . 5 % 30 . 5 % Thus, at 10 am pipe P,Q and R filled 30.5% of the cistern. Rest of cistern to be filled = 100 - 30.5 = 69.5% Now, the time taken by P,Q,R and S together to fill the remaining capacity of the cistern = 69.5 / (5+4+2.5+2) = 5 Hours and 9 minutes(approx). Therefore, total time =4 hrs + 5hrs 9 mins = 9 hrs and 9 mins It means cistern will be filled up at 3:09 pm

Question 13

P is 30% more efficient than Q. How much time will they, working together, take to complete a job which P alone could have done in 23 days?

Accepted Answer

Ratio of times taken by P & Q = 100 : 130 = 10:13 Let Q takes x days to do the work Then, 10:13 :: 23:x => x = 23x13/10 => x = 299/10 P's 1 day's work = 1/23 Q's 1 day's work = 10/299 (P+Q)'s 1 day's work = (1/23 + 10/299) = 23/299 = 1/13 Hence, P & Q together can complete the work in 13 days.

Question 14

9 men and 12 boys finish a job in 12 days, 12 men and 12 boys finish it in 10 days. 10 men and 10 boys shall finish it in how many days ?

Accepted Answer

9M + 12B ----- 12 days ...........(1) 12M + 12B ------- 10 days........(2) 10M + 10B -------? 108M + 144B = 120M +120B 24B = 12M => 1M = 2B............(3) From (1) & (3) 18B + 12B = 30B ---- 12 days 20B + 10B = 30B -----? => 12 days.

Question 15

A contractor undertake to finish a certain work in 124 days and employed 120 men. After 64 days, he found that he had already done 2/3 of the work. How many men can be discharged so that the work may finish in time ?

Accepted Answer

Days remaining 124 – 64 = 60 days Remaining work = 1 - 2/3 = 1/3 Let men required men for working remaining days be 'm' So men required = (120 x 64)/2 = (m x 60)/1 => m = 64 Men discharge = 120 – 64 = 56 men.

Question 16

Three athletes can complete one round around a circular field in 16, 24 and 36 min respectively. They start running together at same instant then after how much time they will meet to each other for first time ?

Accepted Answer

Given that three athletes can complete one round around a circular field in 16, 24 and 36 min respectively. Now, required time after which they met for the first time = LCM of (16, 24 & 36) min Now, LCM of 16, 24, 36 = 144 minutes = 2 hrs 24 min.

Question 17

A contractor undertook a project to complete it in 20 days which needed 5 workers to work continuously for all the days estimated. But before the start of the work the client wanted to complete it earlier than the scheduled time, so the contractor c…

Accepted Answer

Total work = 100+50 = 150man-days In 8 days 100 man-days work has been completed. Now on 9th and 10th day there will be 25 workers. So in 2 days they wll complete additional 50 man- days work. Thus the work requires 2 more days.

Question 18

A can build a wall in 16 days while B can destroy it in 8 days. A worked for 5 days. Then B joined with A for the next 2 days. Find in how many days could A build the remaining wall ?

Accepted Answer

Now, Total work = LCM(16, 8) = 48 A's one day work = + 48/16 = + 3 B's one day work = - 48/8 = -6 Given A worked for 5 days to build the wall => 5 days work = 5 x 3 = + 15 2days B joined with A in working = 2(3 - 6) = - 6 Remaining Work of building wall = 48 - (15 - 6) = 39 Now this remaining work will be done by A in = 39/3 = 13 days.

Question 19

A and B can do a piece of work for Rs 1540. Find the difference between the wages of C and B for the same work If A can do the work in 12 days and B can do the same work in 8 days and with the help of C, A and B can do the same work in 2 days?

Accepted Answer

From the given data, Day Capacity A -> 12 2 B -> 8 3 2 A + B + C -> 2 12 => Capacity of C = 12 - 5 = 7 Ratio of capacity of A : B : C = 2 : 3 : 7 Difference of wages of C & B = 4/5 x 1540 = 4 x 308 = Rs. 1232

Question 20

Time taken by P alone to finish a work is 50% more than the time taken by P and Q together. Q is thrice as efficient as R. If Q and R together can complete the work in 22.5 days, then how many days will P alone take to complete the work ?

Accepted Answer

We know that Time is inversely proportional to Efficiency Here given time ratio of P & P+Q as P/P+Q = 150/100 = 3:2 Efficiency ratio of P & Q as P:Q = 2:1 ....(1) Given Efficiency ratio of Q & R as Q:R = 3:1 ....(2) From (1) & (2), we get P:Q:R = 6:3:1 P alone can finish the work in 22.5(3+1)/6 = 15 days.

Time and Work Questions