**Answer**: Option: A

**Explanation**:

B takes x days to do the work

Therefore, A takes (2 × \(\frac{3}{4}\))xi.e.., 3x/2 days to do it

Now , (A +B)’s 1 day’s work = \(\frac{1}{18}\)

Therefore, \(\frac{1}{x}\) + \(\frac{2}{3}\)x = \(\frac{1}{18}\) or x =30

**2. 12 Men or 18 women can reap a field in 14 days. The number of days that 8 men and 16 women will take to reap it?**

**Answer**: Option: D

**Explanation**:

12 men = 18 women or 1 man = \(\frac{3}{2}\) women

Therefore 8 men + 16 women = (8 × \(\frac{3}{2}\) + 16) women i.e.., 28 women

Now 18 women can reap the field in 14 days

Therefore, 28 women can reap it in = 9 days

**3. If 3 men or 4 women can construct a wall in 43 days, then the number of days that 7 men and 5 women take to construct it is?**

**Answer**: Option: A

**Explanation**:

3 men = 4 women or 1 man = \(\frac{4}{3}\) women

Therefore 7 men + 5 women = (7 × \(\frac{4}{3}\) + 5)women i.e.., 43/3 women

4 women can construct the wall in 43 days

Therefore, \(\frac{43}{3}\) women can construct it in = 12 days

**4. 10 men can finish a piece of work in 10 days. Whereas it takes 12 women to finish it in 10 days if 15 men and 6 women undertake to complete the work. How many days will they take to complete it?**

**Answer**: Option: C

**Explanation**:

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. 8 Children and 12 men complete a certain piece of work in 9 days. If each child takes twice the time taken by man to finish the work. In how many days will 12 men finish the same work?**

**Answer**: Option: D

**Explanation**:

2 children = 1 man

Therefore (8 children +12 men) = 16 men

Now fewer men more days 12: 16:: 9: x

Therefore, x = (\(\frac{144}{12}\)) = 12 days

**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**:

(A+ B)’s 20 day’s work =(20 x \(\frac{1}{30}\)) = \(\frac{2}{3}\)

Remaining work = (1 – \(\frac{2}{3}\)) = \(\frac{1}{3}\) \(\frac{1}{3}\) work is done by A in 20 days

Whole work can be done by A in (3 x 20)days i.e.., 60 days

**3. A can complete a job in 9 days. B in 10 days and C in 15 days. B and C start the work and are forced to leave after 2 days. The time taken to complete the remaining work is?**

**Answer**: Option: A

**Explanation**:

(B + C)’s 2 day’s work = 2 (1/10 + 1/15) = 1/3 Remaining work = (1 – \(\frac{1}{3}\)) = \(\frac{2}{3}\) \(\frac{1}{9}\) work is done by A in 1 day Therefore \(\frac{2}{3}\) work is done by A in (9 x \(\frac{2}{3}\)) = 6 days

**4. A, B and C together earn Rs.150 per day while A and C together earn Rs. 94 and B and C together earn Rs. 76. The daily earning of C is?**

**Answer**: Option: D

**Explanation**:

B’s daily earning = RS.(150 -94) = Rs. 56

A’s daily earning = Rs.(150 -76) = Rs.74

C’s daily earning = Rs.[150 – (56+74)] = Rs. 20

**5. A can do a certain job in 12 days. B is 60% more efficient than A. Then Number of days it takes B to do the same piece of work is?**

**Answer**: Option: C

**Explanation**:

Ratio of times taken by A and B = 160 : 100 = 8 : 5

If A takes 8 days B takes 5 days

If A takes 12 days, B takes =( 7 \(\frac{5}{8}\) x 12) = 7 \(\frac{1}{2}\) days

**Answer**: Option: B

**Explanation**:

Work to be done by C = (1 – \(\frac{7}{11}\)) = \(\frac{4}{11}\)

Therefore, (A +B) = C = \(\frac{7}{11}\) : \(\frac{4}{11}\) = 7 : 4

Therefore C’s share = Rs.(550 x \(\frac{4}{11}\)) = Rs. 200

**2. 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**

**Answer**: Option: B

**Explanation**:

Umesh’s 5 day’s work = 5 x \(\frac{1}{15}\) = 1/3

Remaining work = (1 – \(\frac{1}{3}\)) = \(\frac{2}{3}\) (\(\frac{1}{10}\) + \(\frac{1}{15}\)) work is done by both in 1 day

Therefore 2/3 work is done by both in (6 x \(\frac{2}{3}\)) = 4days.

The work was completed in 9 days

**3. Twelve men can complete a work in 8 days. Three days after they started the work, 3 more men joined them. In how many days will all of them together complete remaining work?**

**Answer**: Option: D

**Explanation**:

1 man’s one day’s work = \(\frac{1}{96}\) 12 men’s 3 day’s work = (3 x \(\frac{1}{8}\)) = \(\frac{3}{8}\)

Remaining work = (1 – \(\frac{3}{8}\)) = \(\frac{5}{8}\) 15 men’s 1 day’s work = \(\frac{15}{96}\)

Now 15/96 work is done by them in 1day

Therefore 5/8 work will be done by them in (\(\frac{96}{15}\) x \(\frac{5}{8}\)) i.e., 4 day

**4. X and Y can do a piece of work in 20 days and 12 days respectively. X started the work alone and then after 4 days Y joined him till the completion of the work. How long did the work last?**

**Answer**: Option: B

**Explanation**:

Work done by X in 4 days = (\(\frac{1}{20}\) * 4) = \(\frac{1}{5}\)

Remaining work = (1 – \(\frac{1}{5}\)) = \(\frac{4}{5}\)

(X + Y)’s 1 day work = (\(\frac{1}{20}\) + \(\frac{1}{12}\)) = \(\frac{2}{15}\)

Now, 2/15 work is done by X and Y in 1 day.

So, 4/5 work will be done by X and Y in (\(\frac{15}{2}\) * \(\frac{4}{5}\)) = 6 days.

Hence, total time taken = (6 + 4) = 10 days.

**5. A and B can together do a price of work in 15 days. B alone can do it in 20 days. In how many days can A alone do it?**

**Answer**: Option: D

**Explanation**:

A’s 1 day’s work = (\(\frac{1}{15}\) – \(\frac{1}{20}\)) = \(\frac{1}{60}\)

Therefore, A alone can finish = 60 days