**Answer**: Option: B

**Explanation**:

Kim’s wages : David’s wages = Kim’s 1 day work : David’s 1 day work = \(\frac{1}{3}\) : \(\frac{1}{2}\) = 2:3

Kim’s share = \(\frac{2}{5}\) * 150 = Rs. 60

**2. 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 to C?**

**Answer**: Option: B

**Explanation**:

C’s 1 day’s work = \(\frac{1}{3}\) – (\(\frac{1}{6}\) + \(\frac{1}{8}\)) = \(\frac{1}{3}\) – \(\frac{7}{24}\) = \(\frac{1}{24}\)

A’s wages : B’s wages : C’s wages

\(\frac{1}{6}\) : \(\frac{1}{8}\): \(\frac{1}{24}\) = 4:3:1

C’s share = \(\frac{1}{8}\) * 3200 = Rs. 400

**3. A and B together can complete a work in 12 days. A alone can complete it in 20 days. If B does the work only for half a day daily, then in how many days A and B together will complete the work?**

**Answer**: Option: C

**Explanation**:

B’s 1 day work = (\(\frac{1}{12}\) – \(\frac{1}{20}\)) = 1/30

Now, (A + B)’s 1 day work = (\(\frac{1}{20}\) + \(\frac{1}{60}\)) = \(\frac{1}{15}\)

So, A and B together will complete the work in 15 days

**4. A, B and C can do a piece of work in 20, 30 and 60 days respectively. In how many days A do the work if he is assisted by B and C on every third day?**

**Answer**: Option: B

**Explanation**:

A’s 2 day’s work = (\(\frac{1}{20}\) * 2) = \(\frac{1}{10}\)

(A + B + C)’s 1 day work = (\(\frac{1}{20}\) + \(\frac{1}{30}\) + \(\frac{1}{60}\)) = \(\frac{1}{10}\)

Work done in 3 days = (\(\frac{1}{10}\) + \(\frac{1}{10}\)) = \(\frac{1}{5}\)

Now, \(\frac{1}{5}\) work is done in 3 days.

Whole work will be done in (3 * 5) = 15 days.

10 men = 12 women or 1 man = \(\frac{6}{5}\) women

Therefore 15 men + 6 women = (15 x \(\frac{6}{5}\) + 6)women i.e,, 24 women

Now 12 women can do the work in 10 days

Therefore, 24 women can do it in = 5 days

**5. 20 women can do a work in 9 days. After they have worked for 6 days. 6 more men join them. How many days will they take to complete the remaining work?**

**Answer**: Option: B

**Explanation**:

(20 * 16) women can complete the work in 1 day.

1 woman’s 1 day work = \(\frac{1}{320}\)

(16 * 15) men can complete the work in 1 day

1 man’s 1 day work = \(\frac{1}{240}\)

So, required ratio = \(\frac{1}{240}\) : \(\frac{1}{320}\)

**Answer**: Option: A

**Explanation**:

(A +B)’s 5 days work = 5 (\(\frac{1}{10}\) +\(\frac{1}{20}\)) = ¾

Remaining work =(1 –\(\frac{3}{4}\)) = ¼ \(\frac{1}{20}\)work is done by B in 1 day.

Therefore, ¼ work is done by B in (20 x \(\frac{1}{4}\))i.e.., 5 days

**2. A and B can together finish a work in 30 days. They worked for it for 20 days and then B left. The remaining work was done by A alone in 20 more days. Alone can finish the work in?**

**Answer**: Option: D

**Explanation**:

1 man’s 1 day work = 1/100

(10 men + 15 women)’s 1 day work = \(\frac{1}{6}\)

15 women’s 1 day work = (\(\frac{1}{6}\) – \(\frac{10}{100}\)) = \(\frac{1}{15}\)

1 woman’s 1 day work = \(\frac{1}{225}\)

1 woman alone can complete the work in 225 days.

**3. 12 men can complete a piece of work in 4 days, while 15 women can complete the same work in 4 days. 6 men start working on the job and after working for 2 days, all of them stopped working. How many women should be put on the job to complete the remaining work, if it so to be completed in 3 days?**

**Answer**: Option: A

**Explanation**:

1 man’s 1 day work = \(\frac{1}{48}\); 1 woman’s 1 day work = 1/60.

6 men’s 2 day’s work = \(\frac{6}{48}\) * 2 = \(\frac{1}{4}\).

Remaining work = (1 – \(\frac{1}{4}\)) = \(\frac{3}{4}\)

Now, \(\frac{1}{60}\) work is done in 1 day by 1 woman.

So, \(\frac{3}{4}\) work will be done in 3 days by (60 * \(\frac{3}{4}\) * \(\frac{1}{3}\)) = 15 women

**4. A man, a woman and a boy can complete a job in 3, 4 and 12 days respectively. How many boys must assist 1 man and 1 woman to complete the job in 1/4 of a day?**

**Answer**: Option: D

**Explanation**:

(1 man + 1 woman)’s 1 day work = (\(\frac{1}{3}\) + \(\frac{1}{4}\)) = 7/12 Work done by 1 man and 1 woman in \(\frac{1}{4}\) day = (\(\frac{7}{12}\) * \(\frac{1}{4}\)) = \(\frac{7}{48}\)

Remaining work = (1 – \(\frac{7}{48}\)) = \(\frac{41}{48}\)

Work done by 1 boy in \(\frac{1}{4}\) day = ( \(\frac{1}{12}\) * \(\frac{1}{4}\)) = \(\frac{1}{48}\)

Number of boys required = \(\frac{41}{48}\) * 41 = 41.

**5. 3 men, 4 women and 6 children can complete a work in 7 days. A woman does double the work a man does and a child does half the work a man does. How many women alone can complete this work in 7 days?**

**Answer**: Option: A

**Explanation**:

Let 1 woman’s 1 day work = x.

Then, 1 man’s 1 day work = \(\frac{X}{2}\) and 1 child’s 1 day work \(\frac{X}{4}\).

So, (\(\frac{3X}{2}\) + 4x + + \(\frac{6X}{4}\)) = \(\frac{1}{7}\)

\(\frac{28X}{4}\) = \(\frac{1}{7}\) => x = \(\frac{1}{49}\)

1 woman alone can complete the work in 49 days.

So, to complete the work in 7 days, number of women required = \(\frac{49}{7}\) = 7.

**Answer**: Option: A

**Explanation**:

1 man’s 1 day work = \(\frac{1}{108}\)

12 men’s 6 day’s work = \(\frac{1}{9}\) * 6 = \(\frac{2}{3}\)

Remaining work = 1 – \(\frac{2}{3}\) = \(\frac{1}{3}\)

18 men’s 1 day work = 1/108 * 18 = \(\frac{1}{6}\)

\(\frac{1}{6}\) work is done by them in 1 day.

\(\frac{1}{3}\) work is done by them in 6 * \(\frac{1}{3}\) = 2 days.

**2. A take twice as much time as B or thrice as much time to finish a piece of work. Working together, they can finish the work in 2 days. B can do the work alone in?**

**Answer**: Option: B

**Explanation**:

Suppose A, B and C take x, \(\frac{X}{2}\) and \(\frac{X}{3}\) respectively to finish the work.

Then, (\(\frac{1}{X}\) + \(\frac{2}{X}\) + \(\frac{3}{X}\)) = 1/2

\(\frac{6}{X}\) = \(\frac{1}{2}\) => x = 12

So, B takes 6 hours to finish the work.

**3. 10 women can complete a work in 7 days and 10 children take 14 days to complete the work. How many days will 5 women and 10 children take to complete the work?**

**Answer**: Option: C

**Explanation**:

1 women’s 1 day work = \(\frac{1}{70}\)

1 child’s 1 day work = \(\frac{1}{140}\)

(5 women + 10 children)’s 1 day work

= (\(\frac{5}{10}\) + \(\frac{10}{40}\)) = (1/14 + \(\frac{1}{14}\)) = \(\frac{1}{7}\)

5 women and 10 children will complete the work in 7 days.

**4. If 12 men and 16 boys can do a piece of work in 5 days; 13 men and 24 boys can do it in 4 days, then the ratio of the daily work done by a man to that of a boy is?**

**Answer**: Option: A

**Explanation**:

Let 1 man’s 1 day work = x and 1 boy’s 1 day work = y.

Then, 12x + 16y = \(\frac{1}{5}\) and 13x + 24y = 1/4

Solving these two equations, we get:

x = \(\frac{1}{100}\) and y = \(\frac{1}{20}\)

Required ratio = x:y = \(\frac{1}{100}\) : \(\frac{1}{200}\) = 2:1

**5. 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?**

**Answer**: Option: B

**Explanation**:

Let 1 man’s 1 day work = x and 1 woman’s 1 day work = y.

Then, 4x + 6y = \(\frac{1}{8}\) and 3x + 7y = \(\frac{1}{10}\)

Solving these two equations, we get:

x = \(\frac{11}{400}\) and y = \(\frac{1}{400}\)

1 woman’s 1 day work = (\(\frac{1}{400}\) * 10) = \(\frac{1}{40}\).

Hence, 10 women will complete the work in 40 days