**Answer**: Option: A

**Explanation**:

(A +B)’s 5 days work = 5 (\(\frac{1}{10}\) + \(\frac{1}{20}\) ) = ¾

Remaining work =(1 – \(\frac{3}{4}\) ) = \(\frac{1}{4}\) \(\frac{1}{20}\) 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 (\(\frac{1}{10}\) + \(\frac{1}{15}\)) = \(\frac{1}{3}\) 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 =(\(\frac{5}{8}\) x 12) = 7 \(\frac{1}{2}\) days

**Answer**: Option: C

**Explanation**:

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

A’s 10 days work = (10 x \(\frac{1}{8}\)) = \(\frac{1}{8}\)

Remaining work = (1 – \(\frac{1}{8}\)) = \(\frac{7}{8}\)

Therefore 7/8 work is done by A in 42 days.

Whole work will be done by A in (42 x \(\frac{8}{7}\))i.e.., 48 days

Therefore, (A+ B)’s 1 day work = (\(\frac{1}{80}\) + \(\frac{1}{48}\)) = \(\frac{8}{240}\) = \(\frac{1}{30}\).

A and B together can finish it in 30days.

**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 \(\frac{1}{15}\) = \(\frac{1}{3}\)

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: B

**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 days

**4. A is 30% more efficient than B. How much time will they, working together, take to complete a job which A alone could have done in 23 days?**

**Answer**: Option: B

**Explanation**:

Ratio of times taken by A and B = 100:130 = 10:13

Suppose B takes x days to do the work.

x = \(\frac{(23 * 13)}{10}\) = \(\frac{299}{10}\)

A’s 1 day work = \(\frac{1}{23}\); B’s 1 day work = \(\frac{10}{299}\)

(A + B)’s 1 day work = (\(\frac{1}{23}\) + \(\frac{10}{299}\)) = \(\frac{1}{13}\)

A and B together can complete the job in 13 days.

**5. A can finish a work in 18 days B can do the same work in 15 days. B worked for 10 days and left the job. In how many days, A alone can finish the remaining work?**

**Answer**: Option: C

**Explanation**:

B’s 10 day’s work = \(\frac{1}{15}\)* 10 = \(\frac{2}{3}\)

Remaining work = (1 – \(\frac{2}{13}\)) = \(\frac{1}{3}\)

Now, 1/18 work is done by A in 1 day.

1/3 work is done by A in (18 * \(\frac{1}{3}\)) = 6 days.

**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, \(\frac{2}{15}\) work is done by X and Y in 1 day.

So, \(\frac{4}{5}\) 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.

**2. A can do a price of work in 30days while B can do it in 40 days. In how many days can A and B working together do it?**

**Answer**: Option: D

**Explanation**:

(A +B)’s 1 day’s work = (\(\frac{1}{30}\) + \(\frac{1}{40}\)) = \(\frac{7}{120}\)

Time is taken by both to finish the work = \(\frac{120}{7}\) days

= 17 \(\frac{1}{7}\) days.

**3. 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

**4. Ronald and Elan are working on an assignment. Ronald takes 6 hrs to type 32 pages on a computer, while Elan takes 5 hrs 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 Ronald in 1 hour = \(\frac{32}{6}\) = \(\frac{16}{3}\)

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

Number of pages typed by both in 1 hour = (\(\frac{16}{3}\) + 8) = \(\frac{40}{3}\)

Time taken by both to type 110 pages = (110 * \(\frac{3}{40}\)) = 8 \(\frac{1}{4}\) = 8 hrs 15 min

**5.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 Tanys = 125:100 = 5:4

Suppose Tanya takes x days to do the work.

5:4 :: 20:x => x= 16 days.

Hence, Tanya takes 16 days to complete the work.