Question 1

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, the time taken by 15 men and 20 boys in doing the same type of work will be:

Accepted Answer

Let 1 man's 1 day's work = x and 1 boy's 1 day's work = y. Then, 6x + 8y = 1 and 26x + 48y = 1 . 10 2 Solving these two equations, we get : x = 1 and y = 1 . 100 200 (15 men + 20 boy)'s 1 day's work = ❨ 15 + 20 ❩ = 1 . 100 200 4 ∴ 15 men and 20 boys can do the work in 4 days.

Question 2

Sakshi can do a piece of work in 20 days. Tanya is 25% more efficient than Sakshi. The number of days taken by Tanya to do the same piece of work is:

Accepted Answer

Ratio of times taken by Sakshi and Tanya = 125 : 100 = 5 : 4. Suppose Tanya takes x days to do the work. 5 : 4 :: 20 : x ⟹ x = ❨ 4 x 20 ❩ 5 ⟹ x = 16 days. Hence, Tanya takes 16 days to complete the work.

Question 3

A can finish a work in 18 days and B can do the same work in 15 days. B worked for 10 days and left the job. In how many days, A alone can finish the remaining work?

Accepted Answer

B's 10 day's work = ❨ 1 x 10 ❩ = 2 . 15 3 Remaining work = ❨ 1 - 2 ❩ = 1 . 3 3 Now, 1 work is done by A in 1 day. 18 ∴ 1 work is done by A in ❨ 18 x 1 ❩ = 6 days. 3 3

Question 4

A and B together can do a piece of work in 30 days. A having worked for 16 days, B finishes the remaining work alone in 44 days. In how many days shall B finish the whole work alone?

Accepted Answer

Let A's 1 day's work = x and B's 1 day's work = y. Then, x + y = 1 and 16x + 44y = 1. 30 Solving these two equations, we get: x = 1 and y = 1 60 60 ∴ B's 1 day's work = 1 . 60 Hence, B alone shall finish the whole work in 60 days.

Question 5

A, B and C can complete a piece of work in 24, 6 and 12 days respectively. Working together, they will complete the same work in:

Accepted Answer

Formula: If A can do a piece of work in n days, then A's 1 day's work = 1 . n (A + B + C)'s 1 day's work = ❨ 1 + 1 + 1 ❩ = 7 . 24 6 12 24 Formula: If A's 1 day's work = 1 , then A can finish the work in n days. n So, all the three together will complete the job in ❨ 24 ❩ days = 3 3 days. 7 7

Question 6

A can finish a work in 24 days, B in 9 days and C in 12 days. B and C start the work but are forced to leave after 3 days. The remaining work was done by A in:

Accepted Answer

(B + C)'s 1 day's work = ❨ 1 + 1 ❩ = 7 . 9 12 36 Work done by B and C in 3 days = ❨ 7 x 3 ❩ = 7 . 36 12 Remaining work = ❨ 1 - 7 ❩ = 5 . 12 12 Now, 1 work is done by A in 1 day. 24 So, 5 work is done by A in ❨ 24 x 5 ❩ = 10 days. 12 12

Question 7

A can do a piece of work in 4 hours; B and C together can do it in 3 hours, while A and C together can do it in 2 hours. How long will B alone take to do it?

Accepted Answer

A's 1 hour's work = 1 ; 4 (B + C)'s 1 hour's work = 1 ; 3 (A + C)'s 1 hour's work = 1 . 2 (A + B + C)'s 1 hour's work = ❨ 1 + 1 ❩ = 7 . 4 3 12 B's 1 hour's work = ❨ 7 - 1 ❩ = 1 . 12 2 12 ∴ B alone will take 12 hours to do the work.

Question 8

A does 80% of a work in 20 days. He then calls in B and they together finish the remaining work in 3 days. How long B alone would take to do the whole work?

Accepted Answer

Whole work is done by A in ❨ 20 x 5 ❩ = 25 days. 4 Now, ❨ 1 - 4 ❩ i.e., 1 work is done by A and B in 3 days. 5 5 Whole work will be done by A and B in (3 x 5) = 15 days. A's 1 day's work = 1 , (A + B)'s 1 day's work = 1 . 25 15 ∴ B's 1 day's work = ❨ 1 - 1 ❩ = 4 = 2 . 15 25 150 75 So, B alone would do the work in 75 = 37 1 days. 2 2

Question 9

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

Accepted Answer

Ratio of times taken by A and B = 100 : 130 = 10 : 13. Suppose B takes x days to do the work. Then, 10 : 13 :: 23 : x ⟹ x = ❨ 23 x 13 ❩ ⟹ x = 299 . 10 10 A's 1 day's work = 1 ; 23 B's 1 day's work = 10 . 299 (A + B)'s 1 day's work = ❨ 1 + 10 ❩ = 23 = 1 . 23 299 299 13 Therefore, A and B together can complete the work in 13 days.

Question 10

A and B can together finish a work 30 days. They worked together for 20 days and then B left. After another 20 days, A finished the remaining work. In how many days A alone can finish the work?

Accepted Answer

(A + B)'s 20 day's work = ❨ 1 x 20 ❩ = 2 . 30 3 Remaining work = ❨ 1 - 2 ❩ = 1 . 3 3 Now, 1 work is done by A in 20 days. 3 Therefore, the whole work will be done by A in (20 x 3) = 60 days.

Question 11

A man, on tour travel first 160 km, at 64 km/hr. and the next 160km at 80km/hr. the average speed for the first 320 km. of the tour is?

Accepted Answer

Average speed = 2t1 x t2/( t1 + t2) = (2x64x80)/(64+80)km = (2 x 64 x 80 ) / 144 km/hr. =71.11km/hr.

Question 12

By walking at 3/4 of his usual speed, a man reaches his office 20 minute later than usual. this usual time is?

Accepted Answer

At a speed of 3/4 of the usual speed, the time taken is 4/3 of the usual time = (4/3 of usual time ) – (usual time ) = 20min. ⇒ 4x/3 -x = 20 ⇒ x/3 =20 ⇒ x=60 min

Question 13

A man travels 35 km partly at 4 km/hr and at 5 km/hr. If he covers former distance at 5 km/hr and later distance at 4 km/hr, he could cover 2 km more in the same time. The time taken to cover the whole distance at original rate is

Accepted Answer

Suppose the man covers first distance in x hrs. and second distance in y hrs. Then , 4x + 5y = 35 and 5x +4y= 37 Solving these equation , we get X=5 and y=3 Total time taken = (5+3) hrs= 8hrs

Question 14

6 men or 10 women can reap a field in 15 days, then the number of days that 12 men and 5 women will take to reap the same field is :

Accepted Answer

Work done by 6 men = work done by 10 women. Work done by 1 man = work done by 10 / 6 = 5/3 women ∴ 12 men + 5 women = 12 x ( 5 / 3) + 5 = 25 women ∴ W1 x D 1 = W2 x D2 W = women, D=days 10 X 15 = 25 x D2 D2 = 6

Question 15

6 children and 2 men complete a certain piece of work in 6 days. Each child takes twice the time taken by a man to finish the work. In how many days will 5 men finish the same work?

Accepted Answer

6C + 2M = 6days 36C + 12M = 1 days Again 1M = 2C ∴ 36+12X2 = 1 day 60 children can do the work in 1 day Now, 5 men = 10 children ∴ 10 children can do the work in 6 days.

Question 16

2 men or 5 women or 7 boys can finish a work in 469 days, then the number of days taken by 7 men, 5 women and 2 boys to finish the work is :

Accepted Answer

2 men = 7 boys ⇒ 1 man = 7/2 days 5 women = 7 boys ⇒ 1 women = 7/5 boys 7 men + 5 women + 2 boys = 7 x 7/2 + 5 x 7/5 + 2 = 67/2 boys Now, B1 x D1 = B2 x D2 7 X 469 = 67/2 x D2 D2 = 98 days

Question 17

314 weavers weaves 6594 shawls in 1/6 hours. What is the number of shawls weaved per hour by an average weaver?

Accepted Answer

In 1 hour 314 weavers weave = 6594 x 6 shawls In 1 hour 1 weaver weaves = ( 6594 x 6 ) / 314 shawls = 126 shawls

Question 18

The Ratio of efficiencies of A, B and C is 6 : 5 : 4 and if A, B and C received total Rs. 27000 for the whole work. What is the share of C, if the money is distributed in the ratio of amount of work done, individually?

Accepted Answer

Ratio of efficiencies of A,B and C = 6 : 5 : 4 ∴ Share of C = [4/(6+5+4)] x 27000 = 7200

Question 19

If 2 men or 3 women or 4 boys can do a piece of work in 52 days. Then the same piece of work will be done by 1 man, 1 woman and 1 boy in?

Accepted Answer

Work done by 2 men = 3 woman = 4 boys ∴ 1 man = 2 boys 1 woman = 4/3 boys ∴ boys X days = 4 X 52 (boys - days) Again 1 man + 1 woman + 1 boy = 2 + 4/3 + 1 = 13/3 boys B1 x D1 = B2 x D2 B = boys, D = days 4 X 52 = 13/3 x D2 D2 = 48 days

Question 20

A contractor undertook a work to complete in 60 days. But just after 20 days he observed that only 1/5th of the project work had been completed. To complete the work in time (i.e,In rest days) minimum how many workers he had to increase, if there we…

Accepted Answer

Work done = 1/5 remaining work = 4/5 ∴ 4 (20 x 75) = 40 x N N = 150 Therefore 75 men should be increased.

Time and Work Questions