Question 1

X can completed a job in 12 days. If X and Y work together, they can complete the job in 6 2/ 3 days, Y alone can complete the job in

Accepted Answer

X's 1 day's work = 1/12 (X + Y)' s 1 day's work = 3/20 ∴ Y's 1 day's work = (3/20) - (1/12) = 4/60 = 1/15 ∴ Number of day's taken by Y to complete the work = 15 days

Question 2

10 men 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 M1 D1 = M2 D2 ⇒ 10 x 8 = M2 x 1/2 ⇒ M2= 10 x 8 x 2 ∴ M2 = 160

Question 3

3 men can do a piece of work in 6 days. 5 women can do the same work in 18 days. If 4 men and 10 women work together, then how long will it take to finish the work?

Accepted Answer

(3 x 6) men = (5 x 18) women 18 men = 90 women ∴ 1 man = 5 women ∴ 4 men + 10 women = 4 x 5 + 10 = 30 women Given, M1 = 5, M2 = 20, D1 = 18 , W1 = W2 = 1 and D2 = ? According to the formula, M1D1W2 = M2D2W1 ⇒ 5 x 18 x 1 = 30 x D2 x 1 ∴ D2 = 5 x 18/30 = 3 days

Question 4

3 men can do a piece of work in 18 days. 6 children can also do that work in 18 days. 4 men and 4 children together will finish the work in how many days?

Accepted Answer

3 men = 6 children ⇒ 1 man = 2 children ∴ 4 men + 4 children = 4 men + (4/2) men = 6 men Given, M1 = 3, M2 = 6, D1 = 18, W1 = W2 = 1 and D2= ? According to the formula, M1D1W2 = M2D2W1 ⇒ 3 x 18 x 1 = 6 x D2 x 1 ∴ D2 = 3 x 18/6 = 9 days

Question 5

P can do piece of work in 12 days, while Q alone can finish it in 8 days. With the help of R, they can finish the work in 4 days. How long will R take to finish the work alone?

Accepted Answer

P,s 1 day's work = 1/12 Q's 1 day's work = 1/8 (P + Q)'s 1 day's work = (1/12) + (1/8) = (2 + 3)/24 = 5/24 (P + Q + R)'s 1 day's work = 1/4 ∴ R's 1 day's work = (1/4) - (5/24) = (6 - 5)/24 = 1/24 ∴ R will finish the work alone in 24 days. ∴ Required time = 24 days

Question 6

A alone can do a certain job in 15 days, while B alone can do it in 10 days. A started the work and was joined by B after 5 days. The work lasted for how many days?

Accepted Answer

A's 5 days' work = (1/15) x 5 = 1/3 Remaining work = 1 - (1/3) = 2/3 ∴ (A + B)'s 1 day's work = (1/15) + (1/10) = (2 + 3(/30 = 5/30 = 1/6 ∴ 2/3 work will be finished by (A + B) in (2/3) x 6 days or in 4 days . ∴ Total time taken = (5 + 4) days = 9 days

Question 7

A does 20 % less work then B. If A can complete a piece of work in 7 1/ 2h, then B can do it in

Accepted Answer

Let time taken by B = N Efficiency ∝ 1/Time taken So, if B is 100% efficient, then A is 80% efficient. So, 80/100 = N /(15/2) ∴ N = 6 h

Question 8

X can do a work in 16 days. In how many days will the work be completed by Y, if the efficiency of Y is 60% more than that of X?

Accepted Answer

Ratio of time taken by X and Y = 160 : 100 = 16 : 1 Suppose Y takes y days to the work. Then, 1.6 : 1 = 16 : y ∴ y = (16 x 1)/1.6 = 10 days

Question 9

2 men and 3 women finish 25% of the work in 4 days, while 6 men and 14 women can finish the whole work in 5 days, In how many days will 20 women finish it?

Accepted Answer

8M + 12W = 4 days (whole work) ⇒ 32M + 48W = 1 day ................ (1) Again 6M + 14W = 5 days ⇒ 30M + 70W = 1 day ................(2) From eq. (1) and (2) 32M + 48W = 30M +70W ⇒ 2M = 22W ⇒ 1M = 11W Now, 30M + 70W = 1 day (30 X 11 X 70)W = 1 day Therefore 400W requires 1 day to complete the whole work. Thus 20W needs 20 days to complete the whole work.

Question 10

10 men and 15 women finish a work in 6 days. One man alone finishes that work in 100 days. In how many days will one women can finish the work?

Accepted Answer

∵ One man alone finishes te work in 100 days. ⇒ 10 men can finish the work in 10 day. ⇒ 15 women can finish work in one days = 1/6 - 1/10 = 1/15 work ⇒ 15 women finish the whole work in 15 days ∴ 1 women finishes the whole work in = 15 x 15 = 225 days

Question 11

A, B and C contract a work for Rs. 550. Together A and B are supposed to do 7/11 of the work. The share of C should be?

Accepted Answer

Work to be done by C = (1 - 7/11) = 4/11 ∴ (A + B) : C = 7/11 : 4/11 = 7 : 4 ∴ C's share = Rs. 550 x (4/11) = Rs. 200

Question 12

A and B separately can complete a work in 6 days and 3 days respectively. If they work together, then in how many days will they complete the work?

Accepted Answer

Work completed by A + B in one day = 1/6 + 1/3 = 1/2 ∴ Time taken by A + B to complete the work = 2 days.

Question 13

Ram, Dilip and Shekhar can complete a work in 20 days. If Ram and Dilip together can complete the same work in 30 days, then how long will Shekhar take to complete it?

Accepted Answer

∵ Work of (Ram + Dilip + Shekhar) for 1 day = 1/20 and work of (Ram + Dilip) for 1 day = 1/30 ∴ Work of Shekhar for 1 day = 1 / 20 - 1 / 30 = 1/60 Hence, Shekhar will complete the work in 60 days.

Question 14

Sunil complete a work in 4 days whereas Dinesh completes the work in 6 days. Ramesh work 1 1/ 2 times as fast as sunil. How many days it will take for the three together to complete the work?

Accepted Answer

Time taken by Ramesh alone = (2/3) x 4 = 8/3 days ∴ Their 1 day's work = (1/4 + 1/6 + 3/8) = 19/24 So, together they can finish the work in 24 /19 days, i.e., 15/19 days.

Question 15

Mahesh and Umesh can complete a work in 10 days and 15 days respectively. Umesh starts the work and after 5 days Mahesh also joins him. In all the work would be completed in?

Accepted Answer

Umesh's 5 day's work = 5 x (1/15) = 1/3 Remaining work = (1 - 1/3) = 2/3 (1/10 + 1/15) work is done by both in 1 day ∴ 2/3 work is done by both in 6 x (2/3) = 4 days Hence, the work was completed in 4 + 5 = 9 days.

Question 16

A can do a piece of work in 80 days. He works at it For 10 days and then B alone finishes the work in 42 days. The two together could complete the work in?

Accepted Answer

A's 10 day's work = (10 x 1/80) = 1/8 Remaining work = (1 - 1/8) = 7/8 ∵ 7/8 work is done by B in 42 days ⇒ Whole work will be done by B in (42 x 8/7) = i .e., 48 days. ∴ (A + B)'s day's work = (1/80 + 1/48) = 8/240 = 1/30 Hence, A and B together can finish it in 30 days.

Question 17

A can do a certain job in 25 days which B alone can do in 20 days. A started the work and was joined by B after 10 days. The work lasted for?

Accepted Answer

A's 10 day's work = 10 x (1/25) = 2/5 Remaining work = 1 - 2/5 = 3/5 Work was done by (A + B) in 1 day = (1/25 + 1/20) = 9/100 ∴ 3/5 work was done by (A + B) in (100/9 x 3/5) = 20/3 days Hence, the work lasted for (10 + 62/3) = 162/3 days.

Question 18

14 men can complete a work in 12 days. 4 days after they started the work, 2 more men joined them. How many days will they take to complete the remaining work?

Accepted Answer

∵ In 12 days work done by 14 men = 1 ∴ In 4 days work done by 14 men = 1 x 4/12 = 1/3 ∴ Remaining work = 1 - 1/3 = 2/3 and number of total men = 14 + 2 = 16 If 1 work is done by 14 men in 12 days ∴ 2/3 work is done by 16 men in 12 x (14/16) x (2/3) = 7 days

Question 19

12 men can complete a work within 9 days. After 3 days they started the work, 6 men joined them to replace 2 men. How many days will they take to complete the remaining work?

Accepted Answer

12 men can complete 1/3 of the work in 3 days and the remaining 2/3 of the work in 6 days. 1 man can complete 2/3 of the work in (12 x 6) = 72 days ∴ (12 - 2 + 6) = 16 men can complete 2/3 of thye work in 72/16 = 41/2 days

Question 20

you can do a piece of work in 8 days, B can do it in 16,While C can do it in 80 days. In how many days they can complete the whole work, working together?

Accepted Answer

Efficiency of A = 12.5% Efficiency of B = 6.25% Efficiency of C = 1.25% Efficiency of (A+ B + C) = (12.5 +6.25 + 1.25) = 20% Required no of days = 100/20 = 5 days

Time and Work Questions