**Answer**: Option: A

**Explanation**:

If A can complete a work in x days and B can complete the same work in y days, then, both

of them together can complete the work in \(\frac{xy}{x + y}\) days

Therefore, here, the required number of days = 12 × \(\frac{24}{36}\) = 8 days.

**2. If 3 persons can do 3 times of a particular work in 3 days, then, 7 persons can do 7 times of that work in **

**Answer**: Option: D

**Explanation**:

That is, 1 person can do one time of the work in 3 days.

Therefore, 7 persons can do 7 times work in the same 3 days itself.

**3. Mangala completes a piece of work in 10 days, Raju completes the same work in 40 days. If both of them work together, then the number of days required to complete the work is **

**Answer**: Option: D

**Explanation**:

If A can complete a work in x days and B can complete the same work in y days, then, both

of them together can complete the work in \(\frac{xy}{x + y}\) days.

That is, the required No. of days = 10 × \(\frac{40}{50}\) = 8 days.

**4. 12 men work 8 hours per day to complete the work in 10 days. To complete the same work in 8 days, working 15 hours a day, the number of men required**

**Answer**: Option: D

**Explanation**:

That is, 1 work done = 12 × 8 × 10

Then, 12 8 × 10 = ? × 15 × 8

? (i.e. No. of men required) = 12 × 8 × \(\frac{10}{15}\) × 10 = 8 days.

**5. If 5 people undertook a piece of construction work and finished half the job in 15 days. If two people drop out, then the job will be completed in**

**Answer**: Option: A

**Explanation**:

That is, half the work done = 5 × 15 × \(\frac{1}{2}\)

Then, 5 × 15 × \(\frac{1}{2}\) = 3 × ? × \(\frac{1}{2}\)

i.e. 5 × 15 = 3 × ?

therefore, ? (No. days required) = 5 × \(\frac{15}{3}\) = 25 days.

**Answer**: Option: B

**Explanation**:

That is, 1 work done = 30 × 7 ×18 = ? × 6 × 30

? (No. of labourers) = 30 × 7 × \(\frac{18}{6}\) × 30 = 21

**2. If 5 girls can embroider a dress in 9 days, then the number of days taken by 3 girls will be **

**Answer**: Option: D

**Explanation**:

That is, 5 × 9 = 3 × ?

? = 5 × \(\frac{9}{3}\) = 15 days

**3. A and B together can plough a field in 10 hours but by himself A requires 15 hours. How long would B take to plough the same field? **

**Answer**: Option: C

**Explanation**:

If A and B together can do a piece of work in x days and A alone can do the same work in y days, then B alone can do the same work in \(\frac{XY}{Y – X}\) days.

Therefore, the No. of hours required by B = 10 × \(\frac{15}{15}\) – 10 = \(\frac{150}{5}\) = 30 hours.

**4. If 12 men can do a piece of work in 24 days, then in how many days can 18 men do the same work? **

**Answer**: Option: D

**Explanation**:

1 work done = 12 × 24

Then, 12 × 24 = 18 × ? days

? days = 12 × \(\frac{24}{18}\) = 16.

**5. A group of workers accepted to do a piece of work in 25 days. If 6 of them did not turn for the work and the remaining workers did the work in 40 days, then the original number of workers was **

**Answer**: Option: D

**Explanation**:

Let the original number of workers be ‘x’

Then, x × 25 = (x – 6) × 40

25x = 40x – 240

240 = 40x – 25x = 15x

x = \(\frac{240}{15}\) = 16.

**Answer**: Option: C

**Explanation**:

8 men = 12 women

1 woman = \(\frac{8}{12}\) men = \(\frac{2}{3}\) men

4 women = \(\frac{2}{3}\) × 4 men = \(\frac{8}{3}\) men

4 men + 4 women = 4 + \(\frac{8}{3}\) men = \(\frac{20}{3}\) men

1 work done = 8 × 10

8 × 10 = \(\frac{20}{3}\) × ?days

? days = 8 × 10 × \(\frac{3}{20}\) = 12 days.

**2. If 8 men can dig a well in 18 days, then the number of days, 12 men will take to dig the same well will be**

**Answer**: Option: A

**Explanation**:

Work done = 8 × 18

Then, 8 × 18 = 12 × ? days

? days = 8 × \(\frac{18}{12}\) = 12 days

**3. 39 men can repair a road in 12 days working 5 hours a day. In how many days will 30 men working 6 hours peer day complete the work?**

**Answer**: Option: B

**Explanation**:

1 work done = 39 × 12 × 5

39 × 12 × 5 = 30 × 6 × ? days

? days = 39 × 12 × \(\frac{5}{30}\) × 6 = 13 days.

**4. A certain number of men can do a work in 40days. If there were 8 men more, it could be finished in 10 days less. How many men were there initially? **

**Answer**: Option: B

**Explanation**:

Let ‘x’ be the initial number of men

Then, 1 work done = x × 40

Then, x × 40 = (x + 8 ) (40 – 10)

40x = 30x + 240

10x = 240

Therefore, x = \(\frac{240}{40}\) = 24 men.

**5. If 4 men or 6 boys can finish a work in 20 days. How long will 6 men and 11 boys take to finish the same work? **

**Answer**: Option: B

**Explanation**:

4 men = 6 boys

Then, 1 boy = \(\frac{4}{6}\) men = \(\frac{2}{3}\) men

11 boys = 2/3 × 11 men = \(\frac{22}{3}\) men

Then, 6 men + 11 boys = 6 + 22/3 men = \(\frac{40}{3}\) men

1 work done = 4 men × 20days

That is, 4 × 20 = \(\frac{40}{3}\) × ? days

? days = 4 × 20 × \(\frac{3}{40}\) = 6 days