Time and Work problems with solutions

Time and Work is an important chapter for quantitative aptitude. Before solving questions below read my previous post on Time and Work concepts

I also made a video to teach basic concepts of this chapter. Questions in this chapter can be solved by two methods, first by fractions and secondly by finding efficiency in percentages. Both methods are equally good but by calculating efficiency in percentages, you can solve the questions quickly. In case you find any difficulty in any question, please leave a comment below.

1.

A can do a job 12 days, B is 60% more efficient than A. How many days B will take to complete the job alone ?

• A.
  6 days
• C.
  8 days
• E.
  None of these

• B.
  7 days
• D.
  7.5 days

• Answer & Explanation

Answer : [D]
Explanation :
⇒ Efficiency of A = 1/12 = 8 ⅓ % per day
⇒ Efficiency of B per day =  8 ⅓ ×  1.6 = 40/3% per day
⇒ Number of days B needs to complete the job = 100 × 3/40 = 7.5 days

2.

Ram can finish a job in 18 days. Shaam can do the same job within 9 days. If they work togother what portoin of work they can complete in a day?

• A.
  1/6
• C.
  1/5

• B.
  1/7
• D.
  2/15

• Answer & Explanation

Answer : [A]
Explanation :
⇒ Ram can do 1/18 part of the job in one day
⇒ Shaam's efficiency is double so he can do 1/9 of the job per day
⇒ Together Ram and Shaam can do 1/18+1/9 = 1/6 of the job per day

3.

Adam can do a job in 15 days, Eve 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.
  1/4
• C.
  1/10

• B.
  7/15
• D.
  8/15

• Answer & Explanation

Answer : [D]
Explanation :
⇒ Adam can do 1/15 of the job per day
⇒ Eve can do 1/20 of the job per day
⇒ If they work together they can do 7/60 of the work together
⇒ Remaining job 1 - 7/60 = 32/60 = 8/15

4.

Ram takes 6 hours to type 32 pages. Shaam takes 5 hours to type 40 pages. In how many hours they will type 110 pages together ?

• A.
  7 hours
• C.
  8 hours

• B.
  8 hours 15 min
• D.
  8 hours 30 mins

• Answer & Explanation

Answer : [B]
Explanation :
⇒Ram can type 32/6 pages per hour
⇒ Shaam can type 8 pages per hour
⇒ They can type 32/6 + 8 = 40/3 pages per hour
⇒ So they will take 110/40 × 3 = 33/4 hours or 8 hours 15 minutes

5.

7 men take 12 days to complete a job. They worked for 5 days, after 5 days 2 men left the job. In how many days 5 men will complete the job ?

• A.
  5 days
• C.
  7 days

• B.
  9 days
• D.
  None of these

• Answer & Explanation

Answer : [D]
Explanation :
⇒7 men can do 1/12 of the job per day
⇒ So after 5 days they have completed 5/12th job. Still 7/12 part of the job is to be completed.
⇒ 5 men can do 1/12 × 5/7 = 5/84 of the job per day
⇒ So they will take 7/12 × 84 /5 = 9 ⅘ days to complete the job

6.

A can do ¼ of the job in 3 days. B can do ⅙ of the same job in 4 days. If they work together Rs 180 is to be paid to them in total, how much A should get ?

• A.
  Rs 64
• C.
  Rs 60

• B.
  Rs 100
• D.
  Rs 120

• Answer & Explanation

Answer : [D]
Explanation :
⇒A can do 1/12 part of the job per day
⇒ B can do 1/24 part of the job per day
⇒ A's efficiency is double than B so he must be paid double than B

7.

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
• C.
  15 days

• B.
  16 days
• D.
  18 days

• Answer & Explanation

Answer : [C]
Explanation :
⇒Efficiency of A = 1/20 = 5% per day
⇒ Efficiency of B = 1/30 = 3.33% per day
⇒ Efficiency of C = 1/60 = 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