Question 1

If 12 man or 18 women can do piece of work in 14 days. How long will 8 men and 16 women take to finish the work?

Accepted Answer

12 men =18 women ⇒ 1 man = 18/12 women ⇒ 8 men = 18/12 x 8 = 12 women Given m1 = 18 M2 = 12 +16 = 28, D1 , D2 = ? and W1 = W2 = 1 According to the formula M1D1W2 = M2D2W1 ⇒ 18 x14 x1= 28 x D2 x1 ∴ D2 = (18 x 14)/28 = 9 days

Question 2

10 man can make a wall in 8 days. How many men required to complete the same work in half days?

Accepted Answer

Given, M1 = 10 D1 = 8, M2 = ? and D2 = 1/2 From M1D1 = M2D2 ⇒ 10 x 8 = M2 x 1/2 ⇒ M2 = 10 x 8 x 2 ∴ M2 = 160

Question 3

6 boys can complete a piece of work in 16 h. In how many hours will 8 boys complete the same work?

Accepted Answer

Given, M1 = 6, M2 = 8 , T1 = 16 h, and T2 = ?, W1 = W2 = 1 According to the formula. M1T1W2 = M2T2W1 ∴ 6 x 16 x 1 = 8 x T2 x 1 ∴ T2 = 16 x 6/8 = 2 x 6 = 12 h

Question 4

In a hostel, there are 120 students and food stock is for 45 days. If 30 new students join the hostel, in how many days will the complete stock be exhausted?

Accepted Answer

Let food stock will be exhausted in x days . Given, m1 = 120, D1 = 45 M2 = 120 + 30 = 150 and D2 = ? Then, using M1D1 = M2D2 ⇒ 120 x 45 = 150 x D2 ∴ D2 = 120 x 45/120 = 36

Question 5

If 5 days take 7 h to pack 35 toys, how many boys can pack 65 toys in 3 h?

Accepted Answer

Given, M1 = 5, M2 = ?, T1 = 7, T2 = 3, W1 = 35 and W2 = 65 According to the formula, M1T1W2 = M2T2W1 ⇒ 5 x 7 x 65= M2 x 3 x 35 ⇒ M2 = (5 x 7 x 65)/(35 x 3) = 65/3 boys

Question 6

A stock of food is enough for 240 men for 48 days. How long will the same stock last for 160 men?

Accepted Answer

M1 = 240, D1 = 48, M2 = 160 and D2 = ? According to the formula, M1D1 = M2D2 ⇒ 240 x 48 = 160 x D2 ∴ D2= (240 x 48)/160 = 72

Question 7

A can do a piece of work in 4 days and B can complete the same work in 12 days. What is the number of days required to do the same work together?

Accepted Answer

A 's 1 day's work = 1/4 B ' s 1 days's work = 1/12 (A+B) ' s day ' s work = 1/4 + 1/12 = (3 + 1)/12 = 4/12 = 1/3 Days required by A and B together to do the work = 1 / (A + B ) ' s day ' s work = 3 days

Question 8

A , B and C can complete a work in 2 h. If A does the job alone in 6 h and B in 5 h, how long will it take for C to finish the job alone?

Accepted Answer

Let C alone can finish the job in T hours. According to the question, Work done by A, B and C in 1h = 1/2 ⇒ 1/6 +1/5 + 1/T = 1/2 ⇒ 1/T = 1/2 - 1/6- 1/5 = (15 - 5- 6)/30 ⇒ 1/T = 4/30 = 2/15 ∴ T = 71/2 h

Question 9

A can copy 75 pages in 25 hours. A and B together can copy 135 pages in 27 hours. In what time can B copy 42 pages?

Accepted Answer

In 25 hours A can copy 75 pages In 1 hour A can copy 75/25 = 3 pages In 25 hours (A and B) can copy = 135/27 = 5 pages ∴ In 1 hour B can copy (5 - 3) = 2 pages ∴ B can copy 42 pages in 21 hours.

Question 10

Mohan can move his lawn in x hours after 2 hour it begins to rain. The unmoved part of the lawn is?

Accepted Answer

∵ Mohan moves the whole lawn in x hours. ⇒ mohan moves in 2 hours = 2/x part of the lawn. ∴ Unmoved part = 1 - 2/x = (x - 2)/ x part

Question 11

The rates of working of A and B are in the ratio 3 : 4. The number of days taken by them to finish the work are in the ratio?

Accepted Answer

Radio of times taken = (1/3) : (1/4) = 4 : 3

Question 12

A does half as much work as B in three-fourth of the time. If the together they take 18 days to complete a work. How much time shall B take to do it?

Accepted Answer

Let B takes N days to do the work ∴ A takes 2 x (3/4) x N = 3N/2 days to do it ∵ (A + B)'s 1 day's work = 1/18 ⇒ 1/N + 2/3N = 1/18 ∴ N = 30

Question 13

A and B together can do a work in 24 days. B alone does its 1/3 part in 12 days. How long will A alone take to do the remaining work?

Accepted Answer

Work done by (A + B) in 1 day = 1/24 Work done by B alone in 1 day = 1/(3 x 12) = 1/36 ∴ Work of A for 1 day = 1/24 - 1/36 = 1/72 After 12 days the remaining work = 1 - 1/3 = 2/3 ∵ 1/72 work is done by A in 1 day ∴ 2/3 work is done by A in (1 x 72)/(1 x 2/3) = 48 days

Question 14

15 men complete a work in 16 days If 24 men are employed then the time require to complete that work will be

Accepted Answer

let the work done be 1 work. Here M1=15, D1=16 W1=W2 =1 M2 =24 D2= ? ∴ According to the formula M1 D1 W2 = M2 D2 W1 ⇒ 15 x 16 x 1 = 24 x D2 X 1 ∴ D1 = 15 X 16/24 = 10 Therefore 10 days are required to complete the work

Question 15

A can complete a piece of work in 18 days and B can complete the same work in half time taken by A. Then, working together, what part of the same work they can complete in a day?

Accepted Answer

A's 1 day's work = 1/18 B's 1 day's work = 1/9 (A + B)'s 1 day's work = 1/9 + 1/18 = 3/18 = 1/6

Question 16

A and B together can do a piece of work in 12 days, while B alone can finish it in 30 days. A alone can finish the work in?

Accepted Answer

(A + B)'s 1 days work = 1/12 B's 1 days work = 1/30 ∴ A's 1 days work = 1/12 - 1/30 = (5 - 2)/60 = 1/20 ∴ A alone can finish the work in 20 days.

Question 17

Aarti can do a piece of work in 6 days. In how many days will she complete three time of work of same type?

Accepted Answer

We have the important relation, More work, More time (days) ∵ A piece of work can be done in 6 days. ∴ Three times of work of same type can be done in 6 x 3 = 18 days

Question 18

A and B can do a piece of work in 6 and 12 days, respectively. They (both) will complete the work in how many days?

Accepted Answer

A's 1 day's work = 1/6 B's 1 day's work = 1/12 (A + B)'s 1 day's work = 1/6 + 1/12 = (2 + 1)/12 = 3/12 = 1/4 Hence, both will complete the work in 4 days.

Question 19

If 3 men and 4 boys can do a piece of work in 8 day, then 6 men and 8 boys can do the same work in?

Accepted Answer

Let the men do the work in a days and the boys in b days. ∴ (3/a) + (4/b) = 1/8 ..... (i) Now, 6/a + 8/b = 2[(3/a) + (4/b)] = 2 x 1/8 = 1/4 So, 6 men and 8 boys can do the same work in 4 days.

Question 20

'A' can do a piece of work in x days and B can do the same work 3x days. To finish the work together they take 12 days. What is the value of x?

Accepted Answer

A's 1 day's work A = 1/x B's 1 day's work B = 1/3x (A + B)'s 1 day's work = (1/x) + (1/3x) = 4/3x And given one day work of both A and B = 1/12 ⇒ 4/3x = 1/12 ⇒ 3x = 48 ⇒ x =16

Time and Work Questions