**Question 31:**

Two men undertake to do a piece of work for Rs.200. One alone could do it in 6 days, the other In 8 days. With the assistance of a boy they finish it in 3 clays. What Is the share of the boy?

[1] Rs.25

[2] Rs.50

[3] Rs.60

[4] Rs.30

**Answer:**

**Explanation: **

1st man's a days work = 3/6, 2nd man's 3 days work = 3/8.

The boy's 3 days' work = 1 — (3/6 + 3/8) = 1/8.

Clearly Rs.200 should be divided amongst them in the proportion of 3/6 : 3/8 : 1/8 or 4 : 3 : 1.

1st man's share = 4/8 of Rs.200 = Rs.100.

2nd man's share = 3/8 of Rs.200 = Rs.75.

The boy's share = 1/8 of Rs.200 = Rs.25.

**Question 32:**

A contract Is to be completed In 56 days and 104 men were set to work, each working 8 hours a day. After 30 days, 2/5 of the work Is finished. How many additional men may be employed so that work may be completed on time?

[1] 180 men

[2] 64 men

[3] 76 men

[4] 96 men

**Answer:**

**Explanation: **

Total number of men =\(104 \times \frac{8}{8} \times \frac{{30}}{{26}} \times \frac{{3/5}}{{2/5}} = 180\)

Therefore, Additional men required = 180 — 104 = 76.

**Question 33:**

Two coal loading machines each working 12 hours per day for 8 days handles 9 tons of coal with an efficiency of 90%. While 3 other coal loading machines at an efficiency of 80% set to handle 12 tons of coal In 6 days. Find how many hours per day each should work?

[1] 12 hrs/day

[2] 16 hrs/day

[3] 20 hrs /day

[4] 18 hrs/day

**Answer:**

**Explanation: **

\(\frac{{{N_1} \times {D_1} \times {H_1} \times {E_1}}}{{{W_1}}} = \frac{{{N_2} \times {D_2} \times {H_2} \times {E_2}}}{{{W_2}}}\) (By chain Rule).

\( = \frac{{2 \times 8 \times 12 \times 90}}{9} = \frac{{3 \times 6 \times {H_2} \times 80}}{{12}} \Rightarrow {H_2} = 16{\rm{ hrs}}/{\rm{day}}\)

**Question 34:**

If the cost of printing a book of 320 leaves with 21 lines On each page and on an average 11 words in each line is Rs.19, then find the cost of printing a book with 297 leaves,28 lines on each page and 10 words In each line.

[1] Rs \(22\frac{3}{8}\)

[2] Rs \(20\frac{3}{8}\)

[3] Rs \(21\frac{3}{8}\)

[4] Rs \(21\frac{3}{4}\)

**Answer:**

**Explanation: **

By chain rule \(\frac{{19}}{{320 \times 21 \times 11}} = \frac{x}{{297 \times 28 \times 10}}\)

\( \Rightarrow x = {\rm{Rs}}.21\frac{3}{8}\)

**Question 35:**

A can do a job in 10 days. B can do in 12 days and C can do in 15 days. All begin together but A leaves the work after 2 days and B leaves 3 days before the work is finished. How long did the work last?

[1] 5 days

[2] 9 days

[3] 4 days

[4] 7 days

**Answer:**

**Explanation: **

Let the job be completed in x days.

Only C remains from the start to the finish of the work. C worked for x days.

A worked for 2 days and B worked for (x-3) days.

\( \Rightarrow \frac{2}{{10}} + \frac{{x - 3}}{{12}} + \frac{x}{{15}} = 1 \Rightarrow x = 7\)

The job is finished in 7 days.