1. A and B working together can complete a work in 12 days, B and C working together will complete the work in 15 days, C and A working together can complete the work in 20 days. If all three work together, in how many days the work can be completed?

A. 10 days B. 8 days C. 13 days D. 12 days

Answer: Option: A
Explanation: Given A + B 's one day work will be [latex]\frac{1}{12}[/latex] Similarly, B + C's one day work will be [latex]\frac{1}{15}[/latex] C + A 's one day work be [latex]\frac{1}{20}[/latex] A + B = [latex]\frac{1}{12}[/latex] ----> (1) B + C = [latex]\frac{1}{15}[/latex] ----> (2) C + A = [latex]\frac{1}{20}[/latex] ----> (3) Adding all the above equation we get 2(A+B+C) = [latex]\frac{1}{12}[/latex] + [latex]\frac{1}{15}[/latex] + [latex]\frac{1}{20}[/latex] => [latex]\frac{5}{60}[/latex] + [latex]\frac{4}{60}[/latex] + [latex]\frac{3}{60}[/latex] => [latex]\frac{12}{60}[/latex] A+B+C = [latex]\frac{12}{120}[/latex] = [latex]\frac{1}{10}[/latex] If all three work together, the work will be completed in 10 days.
2. Adam can do a job in 15 days, John can do the same job in 20 days. If they work together for 4 days on this job. What fraction of job is incomplete?

A. [latex]\frac{1}{4}[/latex] B. [latex]\frac{1}{10}[/latex] C. [latex]\frac{7}{15}[/latex] D. [latex]\frac{8}{15}[/latex]

Answer: Option: D
Explanation: Adam can do 1/15 of the job per day John can do 1/20 of the job per day If they work together they can do [latex]\frac{7}{60}[/latex] of the work together Remaining job 1 - 4*[latex]\frac{7}{60}[/latex] = [latex]\frac{32}{60}[/latex] = [latex]\frac{8}{15}[/latex]
3. If A, B and C can do a job in 20, 30 and 60 days respectively. In how many days A can do the work if B and C help him on every third day?

A. 12 days B. 15 days C. 16 days D. 18 days

Answer: Option: B
Explanation: Efficiency of A = [latex]\frac{1}{20}[/latex] = 5% per day Efficiency of B = [latex]\frac{2}{30}[/latex] = 3.33% per day Efficiency of C = [latex]\frac{1}{60}[/latex] = 1.66% per day In three days A can do 15% of the job himself and B and C do 5% of the job ( 1.66% + 3.33% ) In three days they can do 20% of the job, to do 100% of the job, they need 3 × 5 = 15 days
4. Annie and David can complete the work in 28 and 84 days respectively. If they work together in how many days the work will get completed (in days) ?

A. 21 B. 42 C. 63 D. 20

Answer: Option: A
Explanation: Given that Annie can do the work in 28 days which means Annie can complete 1/ 28th the work in 1 day Given that David can do the work in 84 days which means David can complete 1/ 84th the work in 1 day Let Annie one day work = [latex]\frac{1}{28}[/latex] Let David one day work = [latex]\frac{1}{84}[/latex] Both work together, Together,they finish the work in [latex]\frac{XY}{X + Y}[/latex] days = [latex]\frac{( 28 × 84)}{(28 + 84)}[/latex] = [latex]\frac{2352}{112}[/latex] = 21 days.
5. Albert and Sam can complete a work in 12 and 36 days respectively. If both work together in how many days 50 % of the work will get completed?

A. 4 days B. 5 days C. 4.5 days D. 5.5 days

Answer: Option: C
Explanation: Let the time taken by Albert = A days = 12 days the time taken by Sam = B days = 36 days Albert + Sam together can complete 100 % of the work in: => [latex]\frac{1}{(A + B)}[/latex] = [latex]\frac{1}{(A )}[/latex](1/A) + [latex]\frac{1}{(B)}[/latex] => [latex]\frac{1}{(A + B)}[/latex] = [latex]\frac{1}{(12)}[/latex] + [latex]\frac{1}{(36)}[/latex] => [latex]\frac{1}{(A + B)}[/latex] = [latex]\frac{(36 + 12)}{((12 * 36)}[/latex] => [latex]\frac{1}{(A + B)}[/latex] = [latex]\frac{48}{432}[/latex] Taking reciprocal on both sides A + B = [latex]\frac{432}{48}[/latex] A + B = 9 days Thus 100% of the work is completed in 9 days, 50% of the work is completed in {([latex]\frac{9}{100%}[/latex]) * 50%} days = 4.5 days

1. Somu and Ramu can complete the work in 20 and 30 days respectively. In how many days, 50% of the work will get completed?

A. 5 B. 6 C. 6.5 D. 7.5

Answer: Option: B
Explanation: Let the time taken by Somu= A = 20 days the time taken by Ramu= B = 30 days Then number of days to complete 100% of work by Somu+ Ramutogether: =>[latex]\frac{1}{(A + B)}[/latex] = ([latex]\frac{1}{a}[/latex]) + ([latex]\frac{1}{b}[/latex]) => [latex]\frac{1}{(A + B)}[/latex] = ([latex]\frac{1}{20}[/latex]) + ([latex]\frac{1}{30}[/latex]) => [latex]\frac{1}{(A + B)}[/latex] = (30 + 20) / (20 × 30) => [latex]\frac{1}{(A + B)}[/latex] = [latex]\frac{50}{600}[/latex] Taking reciprocal on both sides A + B = [latex]\frac{600}{50}[/latex] A + B = 12 days Thus 100% of the work is completed in 12 days, 50% of the work is completed in {([latex]\frac{12}{100%}[/latex]) × 50%} days = 6 days
2. 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?

A. 6 days B. 10 days C. 15 days D. 20 days

Answer: Option: B
Explanation: X’s 1 day’s work = [latex]\frac{1}{20}[/latex] X’s 4 day’s work = [latex]\frac{1}{20}[/latex] × 4 = [latex]\frac{1}{5}[/latex] The remaining work = [latex]\frac{4}{5}[/latex] X and Y’s 1 day work = [latex]\frac{1}{20}[/latex] + [latex]\frac{1}{12}[/latex] = [latex]\frac{4}{30}[/latex] = [latex]\frac{2}{15}[/latex] Therefore, Both together finish the remaining work in [latex]\frac{4/5}{2/15}[/latex] days = [latex]\frac{4}{5}[/latex]× [latex]\frac{15}{2}[/latex] = 6 days Therefore, the total number of days taken to finish the work = 4 + 6 = 10 days.
3. A and B can together finish a work in 30 days. They worked together for 20 days and then B left. After another 20 days, A finished he remaining work. In how many days A alone can finish the job?

A. 40 B. 50 C. 55 D. 60

Answer: Option: D
Explanation: A + B ‘s 1 day’s work = [latex]\frac{1}{30}[/latex] Their 20 day’s work = [latex]\frac{1}{30}[/latex] × 20 = [latex]\frac{2}{3}[/latex] Remaining work = [latex]\frac{1}{3}[/latex] [latex]\frac{1}{3}[/latex] of the work is done by A in 20 days. Then, whole work can be done by A in 3 × 20 = 60 days
4. 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: A + B’s 1 day’s work = 1/30 i.e. A + B = 1/30 --------- (i) 16 A + 44 B = 1 ------ (ii) ( i.e. 1 = the whole work done) Multiplying (i) by 16 and subtracting it from (ii), we get i.e. 16 A + 44 B = 1 16 A + 16B = [latex]\frac{8}{15}[/latex] 28 B = [latex]\frac{7}{15}[/latex] B = [latex]\frac{1}{60}[/latex] i.e. B’s 1 day’s work = [latex]\frac{1}{60}[/latex] Therefore, B alone can finish the work in 60 days.
5. A and B together can do a piece of work in 12 days, which B and C together can do in 16 days. After A has been working at it for 5 days and B for 7 days, C finishes it in 13 days. In how many days C alone will do the work?

A. 16 B. 24 C. 36 D. 48

Answer: Option: B
Explanation: According to the question, A + B’s 1 day’s work = [latex]\frac{1}{12}[/latex] B+ C’s 1 days’ work = [latex]\frac{1}{16}[/latex] A worked for 5 days, B for 7 days and C for 13 days. So, we can assume that, A+ B has been working for 5 days and B+ C has been working for 2 days and C alone for 11 days. i.e. A’s 5 day’s work + B’s 7 day’s work + C’s 13 day’s work = 1 (A+ B)’s 5 days work + (B + C)’s 2 days work + C’s 11 day’s work = 1 [latex]\frac{5}{12}[/latex] + [latex]\frac{2}{16}[/latex] + C’s 11 days work = 1 So, C’s 11 day’s work = 1 – ([latex]\frac{5}{12}[/latex] + [latex]\frac{2}{16}[/latex]) = [latex]\frac{11}{24}[/latex] C’s 1 days’ work = [latex]\frac{11}{24}[/latex] X [latex]\frac{1}{11}[/latex] = [latex]\frac{1}{24}[/latex] Therefore, C alone can finish the work in 24 days.

1. A and B can do a piece of work in 45 days and 40 days respectively. They began to do the work together but A leaves after some days and then B completed the remaining work in 23 days. The number of days after which A left the work was:

A. 6 B. 8 C. 9 D. 12

Answer: Option: C
Explanation: A and B together can finish the work in 45 × 40/85 = [latex]\frac{360}{17}[/latex] days A and B’s 1 day’s work = [latex]\frac{17}{360}[/latex] A’s 1 day’s work = [latex]\frac{1}{45}[/latex] B’s 1 day’s work = [latex]\frac{1}{40}[/latex] B’s 23 day’s work [latex]\frac{1}{40}[/latex] × 23 = [latex]\frac{23}{40}[/latex] Remaining work = 1 – 23/40 = [latex]\frac{17}{40}[/latex] [latex]\frac{17}{40}[/latex] of the work is done by A and B together [latex]\frac{17}{40}[/latex] of the work is done by A and B together in = [latex]\frac{17}{40}[/latex] X [latex]\frac{360}{17}[/latex] = [latex]\frac{17}{40}[/latex] × [latex]\frac{360}{17}[/latex] days = 9 days Therefore, A left after 9 days.
2. A can do a piece of work in 20 days which B can do in 12 days. B worked at it for 9 days. A can finish the remaining work in:

A. 3 days B. 5 days C. 10 days D. 18 days

Answer: Option: B
Explanation: A’ s 1 day’s work = [latex]\frac{1}{20}[/latex] B’s 1 day’s work = latex]\frac{1}{13}[/latex] B’s 9 days work = latex]\frac{1}{12}[/latex] × 9 = [latex]\frac{3}{4}[/latex] Remaining work = latex]\frac{1}{4}[/latex] A can finish the remaining work in = [latex]\frac{1}{4}[/latex] X 20 = [latex]\frac{1}{4}[/latex] ×20 = 5 days.
3. A and B together can complete a work in 3 days. They start together. But, after 2 days, B left the work. If the work is completed after 2 more days, B alone could do the work in

A. 5 days B. 6 days C. 9 days D. 10 days

Answer: Option: B
Explanation: A and B’s 1 day’s work = [latex]\frac{1}{3}[/latex] Their 2 day’s work = [latex]\frac{1}{3}[/latex] × 2 = [latex]\frac{2}{3}[/latex] Remaining work = [latex]\frac{1}{3}[/latex] [latex]\frac{1}{3}[/latex] of the work is finished by A in 2 days Then, the whole work can be finished by A alone in 3 × 2 = 6 days So, A’s 1 day’s work = [latex]\frac{1}{6}[/latex] Therefore, B’s 1 day’s work = [latex]\frac{1}{3}[/latex] – [latex]\frac{1}{6}[/latex] = [latex]\frac{1}{6}[/latex] Therefore, the whole work can be done B alone in 6 days
4. A man, a woman and a boy together complete a piece of work in 3 days. If a man alone can do it in 6 days and a boy alone in 18 days, how long will a woman take to complete the work?

A. 9 days B. 21 days C. 24 days D. 29 days

Answer: Option: A
Explanation: Man + Boy + Woman)’s 1 day’s work = [latex]\frac{1}{3}[/latex] Man’s 1day’s work = [latex]\frac{1}{6}[/latex] Boy’s 1 day’s work = [latex]\frac{1}{18}[/latex] Then, Woman’ 1 day’s work = [latex]\frac{1}{3}[/latex] – ( [latex]\frac{1}{6}[/latex] + [latex]\frac{1}{18}[/latex] ) = [latex]\frac{1}{3}[/latex] – [latex]\frac{4}{18}[/latex] = [latex]\frac{2}{18}[/latex] = [latex]\frac{1}{9}[/latex] Therefore, the Woman alone can finish the work in 9 days
5. A and B together can complete a piece of work in 8 days while B and C together can do it in 12 days. All the three together can complete the work in 6 days. In how much time will A and C together complete the work?

A. 8 days B. 10 days C. 12 days D. 20 days

Answer: Option: A
Explanation: A’s 1 day’s work = A + B + C’s 1 day’s work – B + C’s 1 day’s work = [latex]\frac{1}{6}[/latex] – [latex]\frac{1}{12}[/latex] = [latex]\frac{1}{12}[/latex] B’s 1 day’s work = A + B’s 1 day’s work – A’s 1 day’s work = [latex]\frac{1}{8}[/latex] – [latex]\frac{1}{12}[/latex] = [latex]\frac{1}{24}[/latex] C’s 1 day’s work = B+ C’s 1 day’s work – B’s 1 day’s work = [latex]\frac{1}{12}[/latex] – [latex]\frac{1}{24}[/latex] = [latex]\frac{1}{24}[/latex] A +B’ 1 day’s work = [latex]\frac{1}{12}[/latex] + [latex]\frac{1}{24}[/latex] = [latex]\frac{3}{24}[/latex] Therefore, A and C together will finish the whole work in [latex]\frac{24}{3}[/latex] = 8 days