1. Ramesh can complete a work in 12 days, working 7 hours a day. Suresh can complete the same work in 8 days, working 9 hours a day. If Ramesh and Suresh work together working 7 hours a day, in how many days can they complete the work?

A. 7 * [latex]\frac{3}{23}[/latex] B. 5 * [latex]\frac{7}{13}[/latex] C. 6 * [latex]\frac{5}{13}[/latex] D. 6 * [latex]\frac{6}{11}[/latex]

Answer: Option: B
Explanation: Ramesh can finish the work in 12 * 7 = 84 hours Amount of work he can complete in 1 hour = [latex]\frac{1}{84}[/latex] Suresh can finish the same work in 8 * 9 = 72 hours Amount of work he can complete in 1 hour = [latex]\frac{1}{72}[/latex] hours Work done by both of them in 1 hour = = [latex]\frac{1}{84}[/latex] + [latex]\frac{1}{72}[/latex] = [latex]\frac{13}{504}[/latex] Ramesh and Suresh together can complete the work in [latex]\frac{504}{13}[/latex] i.e. 504/13 * 1/7 = [latex]\frac{72}{13}[/latex] i.e. 5 * [latex]\frac{7}{13}[/latex] 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?

A. 35 B. 48 C. 52 D. 58

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?

A. 6 [latex]\frac{1}{2}[/latex] days B. 7 days C. 9 [latex]\frac{1}{2}[/latex] days D. 12 days

Answer: Option: D
Explanation: Daughter’s 1 day’s work = ([latex]\frac{1}{3}[/latex] – [latex]\frac{1}{4}[/latex] ) = 1/12 Daughter alone can do the work in [latex]\frac{12}{1}[/latex] = 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?

A. 8 B. 7 C. 4 D. 5

Answer: Option: D
Explanation: (P + Q)'s 1 day's work = [latex]\frac{1}{4}[/latex] , P's 1 day's work = [latex]\frac{1}{20}[/latex] Q's 1 day's work = ([latex]\frac{1}{4}[/latex] – [latex]\frac{1}{20}[/latex] ) = ([latex]\frac{4}{20}[/latex] ) = ([latex]\frac{1}{5}[/latex] ) 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.

A. I only B. II only C. III only D. I or II or III

Answer: Option: D
Explanation: Clearly, I only gives the answer. Similarly, II only gives the answer. And, III only gives the answer.

1. 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.

A. I alone sufficient while II alone not sufficient to answer B. II alone sufficient while I alone not sufficient to answer C. Either I or II alone sufficient to answer D. Both I and II are not sufficient to answer

Answer: Option: A
Explanation: B's 1 day's work = = 5 ([latex]\frac{1}{20}[/latex] (A+ B)'s 1 day's work = [latex]\frac{1}{7}[/latex] I. (A + B)'s 5 day's work = [latex]\frac{5}{7}[/latex] Remaining work = 1 - [latex]\frac{5}{7}[/latex] = [latex]\frac{2}{7}[/latex] [latex]\frac{2}{7}[/latex] 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 :

A. 4 days B. 6 days C. 8 days D. 12 days

Answer: Option: D
Explanation: A + B + C)'s 1 day's work = [latex]\frac{1}{6}[/latex] (A + B)'s 1 day's work = [latex]\frac{1}{8}[/latex] (B + C)'s 1 day's work = [latex]\frac{1}{12}[/latex] (A + C)'s 1 day's work = 2 X [latex]\frac{1}{6}[/latex] - [latex]\frac{1}{8}[/latex] + [latex]\frac{1}{12}[/latex] = [latex]\frac{1}{3}[/latex] - [latex]\frac{5}{24}[/latex] = [latex]\frac{3}{24}[/latex] = [latex]\frac{1}{8}[/latex]
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?

A. 30 days B. 40 days C. 60 days D. 70 days

Answer: Option: C
Explanation: Let A's 1 day's work = x and B's 1 day's work = y. Then, x + y = [latex]\frac{1}{30}[/latex] and 16x + 44y = 1. Solving these two equations, we get x = [latex]\frac{1}{60}[/latex] and y = [latex]\frac{1}{60}[/latex] B's 1 day's work = [latex]\frac{1}{60}[/latex]
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:

A. 4 days B. 6 days C. 8 days D. 12 days

Answer: Option: B
Explanation: Suppose A, B and C take x, [latex]\frac{X}{2}[/latex] and [latex]\frac{x}{3}[/latex] days respectively to finish the work. Then, [latex]\frac{1}{x}[/latex] + [latex]\frac{2}{x}[/latex] + [latex]\frac{3}{x}[/latex] = [latex]\frac{1}{2}[/latex] [latex]\frac{6}{x}[/latex] = [latex]\frac{1}{2}[/latex] 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 :

A. 8 days B. 10 days C. 12 days D. 15 days

Answer: Option: A
Explanation: (A + B)'s 1 day's work = [latex]\frac{1}{15}[/latex] + [latex]\frac{1}{10}[/latex] = [latex]\frac{1}{6}[/latex] Work done by A and B in 2 days = [latex]\frac{1}{6}[/latex] x 2 = [latex]\frac{1}{3}[/latex] Remaining work = 1 - [latex]\frac{1}{3}[/latex] = [latex]\frac{2}{3}[/latex] Now, [latex]\frac{1}{15}[/latex] work is done by A in 1 day [latex]\frac{2}{3}[/latex] work will be done by a in 15 x [latex]\frac{2}{3}[/latex] = 10 days. Hence, the total time taken = (10 + 2) = 12 days

1. A works twice as fast as B. If B can complete a work in 12 days independently, the number of days in which A and B can together finish the work in :

A. 4 days B. 6 days C. 8 days D. 18 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 = [latex]\frac{1}{12}[/latex] A's 1 day's work = [latex]\frac{1}{6}[/latex] (A + B)'s 1 day's work = [latex]\frac{1}{6}[/latex] + [latex]\frac{1}{12}[/latex] = [latex]\frac{3}{12}[/latex] = [latex]\frac{1}{4}[/latex]
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?

A. 3 : 4 B. 4 : 3 C. 5 : 3 D. Data inadequate

Answer: Option: B
Explanation: (20 x 16) women can complete the work in 1 day. 1 woman's 1 day's work = = [latex]\frac{1}{320}[/latex] (16 x 15) men can complete the work in 1 day. 1 man's 1 day's work = [latex]\frac{1}{240}[/latex] So, required ratio = [latex]\frac{1}{240}[/latex]: [latex]\frac{1}{320}[/latex] = [latex]\frac{1}{3}[/latex] : [latex]\frac{1}{4}[/latex] 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?

A. 7 hours 30 minutes B. 8 hours C. 8 hours 15 minutes D. 8 hours 25 minutes

Answer: Option: C
Explanation: Number of pages typed by Ravi in 1 hour = [latex]\frac{32}{6}[/latex] = [latex]\frac{16}{3}[/latex] Number of pages typed by Kumar in 1 hour = [latex]\frac{40}{5}[/latex] = 8 Number of pages typed by both in 1 hour = [latex]\frac{16}{3}[/latex] + 8 Time taken by both to type 110 pages = 110 x [latex]\frac{3}{40}[/latex] 8 [latex]\frac{1}{4}[/latex] 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:

A. 15 B. 16 C. 18 D. 25

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 = [latex]\frac{4 × 20}{5}[/latex] 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.

A. I alone sufficient while II alone not sufficient to answer B. II alone sufficient while I alone not sufficient to answer C. Either I or II alone sufficient to answer D. Both I and II are not sufficient to answer

Answer: Option: A
Explanation: B's 1 day's work = [latex]\frac{1}{20}[/latex] (A+ B)'s 1 day's work = [latex]\frac{11}{7}[/latex] I. (A + B)'s 5 day's work = [latex]\frac{5}{7}[/latex] Remaining work = 1 - [latex]\frac{5}{7}[/latex] = [latex]\frac{2}{7}[/latex] [latex]\frac{2}{7}[/latex] work was carried by A. II. is irrelevant.