**Question 11:**

To do a certain piece of work, B would take three times as long as A and C together and C twice as long as A and B together. The three men working together can complete the work in 10 days. How long would B take by himself to complete the same piece of work?

[1] 24 days

[2] 30 days

[3] 40 days

[4] 36 days

**Answer:**

**Explanation: **

By the question, 3 times B's daily work = (A + C)'s daily work.

Add B's daily work to both sides.

=> 4 times B's daily work = (A + B + C)'s daily work = 1/10.

=>B's daily work = 1/40 .... (1)

Also, 2 times C's daily work = (A + B)'s daily work.

Add C's daily work to both sides.

=>3 times C's daily work = (A + B + C)'s daily work = 1/10.

=>C's daily work = 1/30 .... (2)

Now A's daily work = 1/10 — (1/40 + 1/30) = 1/24 ...(3)

=>A, B and C can do the work in 24, 40 and 30 days respectively.

**Question 12:**

A and B working separately can finish a work in 8 and 12 days respectively. If they work for a day alternately (beginning with A), then in how many days will the work be completed?

[1] 9 days

[2] 9.5 days

[3] 10 days

[4] 9.8 days

**Answer:**

**Explanation: **

A's one day's work = 1/8.

Then B comes and does 1/12 of the whole work. Hence at the end of two days,

(1/8 + 1/12 = 5/24) of the whole work has been done.

in the next 2 days, 5/24 of the whole work will again be done.

=>In these 4 days, 5/24 + 5/24 = 10/24 of the work has been done.

Again in the next four days, 10/24 of the work will be done.

=>In these 4 + 4 = 8 days, 10/24 + 10/24 = 20/24 of the whole work will be done.

Remaining work = 1 — 20/24 = 4/24 = 1/6th of the work.

Now A does 1/8th of the work in one day.

Hence remaining work = 116 — 1/8 = 1/24.

This will be now completed by B. B does 1/12 of the work in 1 day.

Hence he will complete 1/24 of the work in 1/24 ÷ 1/12 = 1/2 days.

Hence total time taken = 4 + 4 + 1 + 1/2 = 9.5 days.

**Question 13:**

Raman and Bose working separately can finish a work in 50 and 40 days respectively. They begin the work together and after 10 days, Bose goes away. In how many days will the work be completed by Raman alone?

[1] 27 days

[2] 28 days

[3] 350/17 days

[4] 55/2 days

**Answer:**

**Explanation: **

(Raman's + Bose's) one day's work \( = \frac{1}{{50}} + \frac{1}{{40}} = \frac{9}{{200}}\)

They worked together for 10 days.

Hence their 10 day's work =\(\frac{9}{200}\times 10=\frac{9}{20}\)

Remaining work \( = 1 - \frac{9}{{20}} = \frac{{11}}{{20}}\) This is completed by Raman alone.

Raman will require, \(\frac{{11}}{{20}} \div \frac{1}{{50}} = \frac{{55}}{2}\) days to complete the remaining work.

**Question 14:**

Two men, A and B, working separately can mow a field in 10 and 12 hours respectively. If they work for an hour alternately, B beginning at 9 am, then at what time will the mowing be finished?

[1] 7:30 pm

[2] 8:00 pm

[3] 8:30 pm

[4] 9:00 pm

**Answer:**

**Explanation: **

In the first hour 1 , B mows \(\frac{1}{{12}}\) of the field.

In the second hour, A mows \(\frac{1}{{10}}\) of the field.

In 2 hours, \(\frac{{11}}{{60}}\) of the field is mown.

In 10 hours, \(\frac{{55}}{{60}}\) of the field is mown.

Now remaining work is \(1 - \frac{{55}}{{60}} = \frac{5}{{60}} = \frac{1}{{12}}\)field remains to be mown.

In the 11th hour, B mows remaining\(\frac{1}{{12}}\) of the field.

the total time required is 11 hours.

The work started at 9 am

:. it would be finished at 8.00 pm.

**Question 15:**

25 men can reap a field in 20 days. When should 15 men leave the work, if the whole field is to be reaped in 371/2 days after they leave the work?

[1] after 4 days

[2] after. 6 days

[3] after 5 days

[4] after 3 days

**Answer:**

**Explanation: **

=> 25 men can reap the field in 20 days,

=> 10 men can reap the field in 20 x 25/10 or 50 days.

When 15 men leave the work, 10 men remain and these can reap in 37.5 days

37.5/50 or 3/4 of the field.

Hence all men must work till (1 — 3/4) or 1/4 of the field is reaped.

Now 25 men reap 1/4 of the field in 20/4 or 5 days.

Hence 15 men should leave the work after 5 days.