**Answer**: Option: B

**Explanation**:

Ramesh can finish the work in 12 * 7 = 84 hours

Amount of work he can complete in 1 hour = \(\frac{1}{84}\)

Suresh can finish the same work in 8 * 9 = 72 hours

Amount of work he can complete in 1 hour = \(\frac{1}{72}\) hours

Work done by both of them in 1 hour =

= \(\frac{1}{84}\) + \(\frac{1}{72}\) = \(\frac{13}{504}\)

Ramesh and Suresh together can complete the work in \(\frac{504}{13}\)

i.e. 504/13 * 1/7 = \(\frac{72}{13}\)

i.e. 5 * \(\frac{7}{13}\) days

**2. An employer pays Rs. 30 for each day a worker works, and forfeits Rs. 5 for each day he is idle. At the end of 60 days, a worker gets Rs. 500. For how many days did the worker remain idle? **

**Answer**: Option: C

**Explanation**:

Suppose the worker remained idle for m days. Then, he worked for (60 – m) days.

30 (60 – m) – 5m = 500

1800 – 25m = 500

25m = 1300

m = 52

So, the worker remained idle for 52 days.

**3. A man can do a piece of work in 4 days, but with the help of his daughter, he can do it in 3 days. In what time can his daughter do it alone? **

**Answer**: Option: D

**Explanation**:

Daughter’s 1 day’s work = (\(\frac{1}{3}\) – \(\frac{1}{4}\) ) = 1/12

Daughter alone can do the work in \(\frac{12}{1}\) = 12 days

**4. P and Q together can complete a piece of work in 4 days. If P alone can complete the same work in 20 days, in how many days can Q alone complete that work? **

**Answer**: Option: D

**Explanation**:

(P + Q)’s 1 day’s work = \(\frac{1}{4}\) , P’s 1 day’s work = \(\frac{1}{20}\)

Q’s 1 day’s work = (\(\frac{1}{4}\) – \(\frac{1}{20}\) ) = (\(\frac{4}{20}\) ) = (\(\frac{1}{5}\) )

Hence, Q alone can complete the work in 5 days.

**5. 8 men and 14 women are working together in a field. After working for 3 days, 5 men and 8 women leave the work. How many more days will be required to complete the work?**

I. 19 men and 12 women together can complete the work in 18 days.

II. 16 men can complete two-third of the work in 16 days.

** III. In 1 day, the work done by three men in equal to the work done by four women.**

**Answer**: Option: D

**Explanation**:

Clearly, I only gives the answer.

Similarly, II only gives the answer.

And, III only gives the answer.

I. A completed the job alone after A and B worked together for 5 days.

** II. Part of the work done by A could have been done by B and C together in 6 days.**

**Answer**: Option: A

**Explanation**:

B’s 1 day’s work = = 5 (\(\frac{1}{20}\)

(A+ B)’s 1 day’s work = \(\frac{1}{7}\)

I. (A + B)’s 5 day’s work = \(\frac{5}{7}\)

Remaining work = 1 – \(\frac{5}{7}\) = \(\frac{2}{7}\)

\(\frac{2}{7}\) work was carried by A.

II. is irrelevant.

**2. A and B can do a work in 8 days, B and C can do the same work in 12 days. A, B and C together can finish it in 6 days. A and C together will do it in :**

**Answer**: Option: D

**Explanation**:

A + B + C)’s 1 day’s work = \(\frac{1}{6}\)

(A + B)’s 1 day’s work = \(\frac{1}{8}\)

(B + C)’s 1 day’s work = \(\frac{1}{12}\)

(A + C)’s 1 day’s work = 2 X \(\frac{1}{6}\) – \(\frac{1}{8}\) + \(\frac{1}{12}\)

= \(\frac{1}{3}\) – \(\frac{5}{24}\)

= \(\frac{3}{24}\)

= \(\frac{1}{8}\)

**3. A and B together can do a piece of work in 30 days. A having worked for 16 days, B finishes the remaining work alone in 44 days. In how many days shall B finish the whole work alone?**

**Answer**: Option: C

**Explanation**:

Let A’s 1 day’s work = x and B’s 1 day’s work = y.

Then, x + y = \(\frac{1}{30}\) and 16x + 44y = 1.

Solving these two equations, we get x = \(\frac{1}{60}\) and y = \(\frac{1}{60}\)

B’s 1 day’s work = \(\frac{1}{60}\)

**4. A takes twice as much time as B or thrice as much time as C 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 \(\frac{x}{3}\) days respectively to finish the work.

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

\(\frac{6}{x}\) = \(\frac{1}{2}\)

x = 12

**5. A and B can complete a work in 15 days and 10 days respectively. They started doing the work together but after 2 days B had to leave and A alone completed the remaining work. The whole work was completed in :**

**Answer**: Option: A

**Explanation**:

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

Work done by A and B in 2 days = \(\frac{1}{6}\) x 2 = \(\frac{1}{3}\)

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

Now, \(\frac{1}{15}\) work is done by A in 1 day

\(\frac{2}{3}\) work will be done by a in 15 x \(\frac{2}{3}\) = 10 days.

Hence, the total time taken = (10 + 2) = 12 days

**Answer**: Option: A

**Explanation**:

Ratio of rates of working of A and B = 2 : 1.

So, the ratio of times taken = 1: 2.

B’s 1 day’s work = \(\frac{1}{12}\)

A’s 1 day’s work = \(\frac{1}{6}\)

(A + B)’s 1 day’s work = \(\frac{1}{6}\) + \(\frac{1}{12}\) = \(\frac{3}{12}\) = \(\frac{1}{4}\)

**2. Twenty women can do a work in sixteen days. Sixteen men can complete the same work in fifteen days. What is the ratio between the capacity of a man and a woman?**

**Answer**: Option: B

**Explanation**:

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

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

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

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

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

= \(\frac{1}{3}\) : \(\frac{1}{4}\)

4:3

**3. Ravi and Kumar are working on an assignment. Ravi takes 6 hours to type 32 pages on a computer, while Kumar takes 5 hours to type 40 pages. How much time will they take, working together on two different computers to type an assignment of 110 pages?**

**Answer**: Option: C

**Explanation**:

Number of pages typed by Ravi in 1 hour = \(\frac{32}{6}\) = \(\frac{16}{3}\)

Number of pages typed by Kumar in 1 hour = \(\frac{40}{5}\) = 8

Number of pages typed by both in 1 hour = \(\frac{16}{3}\) + 8

Time taken by both to type 110 pages = 110 x \(\frac{3}{40}\)

8 \(\frac{1}{4}\) hours (or) 8 hours 15 minutes.

**4. Sakshi can do a piece of work in 20 days. Tanya is 25% more efficient than Sakshi. The number of days taken by Tanya to do the same piece of work is:**

**Answer**: Option: B

**Explanation**:

Ratio of times taken by Sakshi and Tanya = 125 : 100 = 5 : 4.

Suppose Tanya takes x days to do the work.

5 : 4 :: 20 : x x = \(\frac{4 × 20}{5}\)

x = 16 days.

**5. A and B together can complete a task in 7 days. B alone can do it in 20 days. What part of the work was carried out by A?**

I. A completed the job alone after A and B worked together for 5 days.

** II. Part of the work done by A could have been done by B and C together in 6 days.**

**Answer**: Option: A

**Explanation**:

B’s 1 day’s work = \(\frac{1}{20}\)

(A+ B)’s 1 day’s work = \(\frac{11}{7}\)

I. (A + B)’s 5 day’s work = \(\frac{5}{7}\)

Remaining work = 1 – \(\frac{5}{7}\) = \(\frac{2}{7}\)

\(\frac{2}{7}\)

work was carried by A.

II. is irrelevant.