# Time and Work Questions Answers

1) A can do a job in 16 days, B can do same job in 12 days. With the help of C they did the job in 4 days. C alone can do the same job in how many days

- 1) \begin{aligned} 6\frac{1}{2}days \end{aligned}
- 2) \begin{aligned} 7\frac{1}{2}days \end{aligned}
- 3) \begin{aligned} 8\frac{3}{5}days \end{aligned}
- 4) \begin{aligned} 9\frac{3}{5}days \end{aligned}

**Ans.**D

**Explanation :**

In this question we having, A's work, B's work and A+B+C work. We need to calculate C's work. We can do it by, (A+B+C)'s work - (A's work + B's work). Let's solve it now: C's 1 day work = \begin{aligned} \frac{1}{4}- \left(\frac{1}{16} +\frac{1}{12} \right) \\ =\left(\frac{1}{4} - \frac{7}{48} \right) \\ = \frac{5}{48} \end{aligned} So C can alone finish the job in 48/5 days, Which is = \begin{aligned} 9\frac{3}{5}days \end{aligned}

2) To complete a work A and B takes 8 days, B and C takes 12 days, A,B and C takes 6 days. How much time A and C will ta

- 1) 24 days
- 2) 16 days
- 3) 12 days
- 4) 8 days

**Ans.**D

**Explanation :**

A+B 1 day work = 1/8 B+C 1 day work = 1/12 A+B+C 1 day work = 1/6 We can get A work by (A+B+C)-(B+C) And C by (A+B+C)-(A+B) So A 1 day work = \begin{aligned} \frac{1}{6}- \frac{1}{12} \\ = \frac{1}{12} \end{aligned} Similarly C 1 day work = \begin{aligned} \frac{1}{6}- \frac{1}{8} \\ = \frac{4-3}{24} \= \frac{1}{24} \end{aligned} So A and C 1 day work = \begin{aligned} \frac{1}{12} + \frac{1}{24} \\ = \frac{3}{24} \= \frac{1}{8} \end{aligned} So A and C can together do this work in 8 days

3) A does half as much work as B in three-fourth of the time. If together they take 18 days to complete the work, how much time shall B take to do

- 1) 40 days
- 2) 35 days
- 3) 30 days
- 4) 25 days

**Ans.**C

**Explanation :**

Suppose B takes x dÃ¡ys to do the work. As per question A will take \begin{aligned} 2* \frac{3}{4} * x = \frac{3x}{2}days \end{aligned} (A+B)s 1 days work= 1/18 1/x + 2/3x = 1/18 or x = 30 days

4) A is thrice as good a workman as B and takes 10 days less to do a piece of work than B takes. B alone can do the whole work

- 1) 15 days
- 2) 10 days
- 3) 9 days
- 4) 8 days

**Ans.**A

**Explanation :**

Ratio of times taken by A and B = 1:3 Means B will take 3 times which A will do in 1 time If difference of time is 2 days, B takes 3 days If difference of time is 10 days, B takes (3/2) * 10 =15 days

5) A can do a piece of work in 15 days and B alone can do it in 10 days. B works at it for 5 days and then leaves. A alone can finish the remaining work

- 1) 5 days
- 2) 6 days
- 3) 7.5 days
- 4) 8.5 days

**Ans.**C

**Explanation :**

B's 5 days work = \begin{aligned} \frac{1}{10}*5 = \frac{1}{2} \ \text{Remaining work =} 1-\frac{1}{2} \ = \frac{1}{2} \ \text{A can finish work =}15*\frac{1}{2} \= 7.5 days \end{aligned}

6) A completes 80% of a work in 20 days. Then B also joins and A and B together finish the remaining work in 3 days. How long does it need for B if he alone completes the wo

- 1) \begin{aligned} 35\frac{1}{2} \end{aligned}
- 2) \begin{aligned} 36\frac{1}{2} \end{aligned}
- 3) \begin{aligned} 37\frac{1}{2} \end{aligned}
- 4) \begin{aligned} 38\frac{1}{2} \end{aligned}

**Ans.**C

**Explanation :**

Work done by A in 20 days = 80/100 = 8/10 = 4/5 Work done by A in 1 day = (4/5) / 20 = 4/100 = 1/25 --- (1) Work done by A and B in 3 days = 20/100 = 1/5 (Because remaining 20% is done in 3 days by A and B) Work done by A and B in 1 day = 1/15 ---(2) Work done by B in 1 day = 1/15 â€“ 1/25 = 2/75 => B can complete the work in 75/2 days = 37 (1/2) days

7) A can do a piece of work in 4 hours . A and C together can do it in just 2 hours, while B and C together need 3 hours to finish the same work. In how many hours B can complete the wor

- 1) 10 hours
- 2) 12 hours
- 3) 16 hours
- 4) 18 hours

**Ans.**B

**Explanation :**

Work done by A in 1 hour = 1/4 Work done by B and C in 1 hour = 1/3 Work done by A and C in 1 hour = 1/2 Work done by A,B and C in 1 hour = (1/4)+(1/3) = 7/12 Work done by B in 1 hour = (7/12)â€“(1/2) = 1/12 => B alone can complete the work in 12 hour

8) A alone can do a piece of work in 6 days and B alone in 8 days. A and B undertook to do it for Rs. 3200. With the help of C, they completed the work in 3 days. How much is to be paid t

- 1) Rs. 300
- 2) Rs. 400
- 3) Rs. 500
- 4) Rs. 600

**Ans.**B

**Explanation :**

C's 1 day's work = \begin{aligned} \frac{1}{3}- \left(\frac{1}{6} +\frac{1}{8} \right) \\ =\left(\frac{1}{3} - \frac{7}{24} \right) \\ = \frac{1}{24} \A:B:C = \frac{1}{6}:\frac{1}{8}:\frac{1}{24} \= 4:3:1 \C's Share = \frac{1}{8}* 3200 \ = 400 \end{aligned} If you are confused how we multiplied 1/8, then please study ratio and proportion chapter, for small information, it is the C ratio divided by total ratio.

9) 4 men and 6 women finish a job in 8 days, while 3 men and 7 women finish it in 10 days. In how many days will 10 women working together finish i

- 1) 30 days
- 2) 40 days
- 3) 50 days
- 4) 60 days

**Ans.**B

**Explanation :**

Let 1 man's 1 day work = x and 1 woman's 1 days work = y. Then, 4x + 6y = 1/8 and 3x+7y = 1/10 solving, we get y = 1/400 [means work done by a woman in 1 day] 10 women 1 day work = 10/400 = 1/40 10 women will finish the work in 40 days

10) A piece of work can be done by 6 men and 5 women in 6 days or 3 men and 4 women in 10 days. It can be done by 9 men and 15 women in how many day

- 1) 3 days
- 2) 4 days
- 3) 5 days
- 4) 6 days

**Ans.**A

**Explanation :**

To calculate the answer we need to get 1 man per day work and 1 woman per day work. Let 1 man 1 day work =x and 1 woman 1 days work = y. => 6x+5y = 1/6 and 3x+4y = 1/10 On solving, we get x = 1/54 and y = 1/90 (9 men + 15 women)'s 1 days work = (9/54) + (15/90) = 1/3 9 men and 15 women will finish the work in 3 days