420+ Solved Time and Work Problems with Solutions and Explanation

Q:

A can finish a work in 18 days and B in 36 days. If they work on it together for 9 days, then what percent of work is left?

A) 33.3	B) 20
C) 75	D) 25

Answer & Explanation Answer: D) 25

Explanation:

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Q:

Prabhas is twice as good a workman as Rana and finishes a piece of work in 3 hours. In how many hours they together could finish that piece of work?

A) 3 hrs	B) 3.5 hrs
C) 2.5 hrs	D) 2 hrs

Answer & Explanation Answer: D) 2 hrs

Explanation:

Given Prabhas is twice as good a workman as Rana.

Prabhas finishes the work in 3 hrs

=> Rana finishes the work in 6 hrs.

Number of hours required together they could finish the work

= 3 x 6 / 3 + 6

= 18/9

= 2 hrs.

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Q:

Raghu can complete a work in 12days working 9 hours a day. Arun can complete the same work in 8 days working 11 hours a day. If both Raghu and Arun work together, working 12 hours a day, in how many days can they complete the work ?

A) $3 \frac{4}{49} d a y s$

B) $12 \frac{4}{49} d a y s$

C) $4 \frac{3}{49} d a y s$

D) $4 \frac{12}{49} d a y s$

A) Option A	B) Option B
C) Option C	D) Option D

Answer & Explanation Answer: C) Option C

Explanation:

Raghu can complete the work in (12 x 9)hrs = 108 hrs.

Arun can complete the work in (8 x 11)hrs = 88 hrs.

Raghu's 1 hrs work = 1/108 and Arun's 1 hrs work = 1/88

(Raghu + Arun)'s 1 hrs work = $(\frac{1}{108} + \frac{1}{88}) = \frac{49}{2376}$

So, both Raghu and Arun will finish the work in $\frac{2376}{49} h r s$

Number of days of 12 hours each= $(\frac{2376}{49} \times \frac{1}{12})$ = $\frac{198}{49} = 4 \frac{3}{49} d a y s$

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Q:

A can do a work in 9 days, B can do a work in 7 days, C can do a work in 5 days. A works on the first day, B works on the second day and C on the third day respectively that is they work on alternate days. When will they finish the work ?

A) [7 + (215/345)] days	B) [6 + (11/215)] days
C) [6 + (261/315)] days	D) [5 + (112/351)] days

Answer & Explanation Answer: C) [6 + (261/315)] days

Explanation:

After day 1, A finishes 1/9 of the work.

After day 2, B finishes 1/7 more of the total work. (1/9) + (1/7) is finished.

After day 3, C finishes 1/5 more of total work. Total finished is 143/315.

So, after day 6, total work finished is 286/315.

Now remaining work = 29 /315

On day 7, A will work again

Work will be completed on day 7 when A is working. He must finish 29/315 of total remaining work.

Since he takes 9 days to finish the total task, he will need 261/315 of the day.

Total days required is 6 + (261/315) days.

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Q:

A town having teenagers(boys & girls) of 5000 requires 150 litre of water per head. It has a tank measuring 20 m × 15 m × 5 m. The water of this tank will sufficient for ____ days.

A) 8	B) 6
C) 4	D) 2

Answer & Explanation Answer: D) 2

Explanation:

Total Water reqduired = 5000 × 150 lit = 750,000 litres = 750 cu.m.

Volume of tank = 20 × 15 × 5 = 1500 Cu.m.

Number of days required =1500/750 = 2 days.

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Q:

45 men working 9 hours per day dig 40 m deep. How many extra men should be put to dig to a depth of 56 m working 7 hours per day ?

A) 36	B) 61
C) 48	D) 54

Answer & Explanation Answer: A) 36

Explanation:

(45 x 9)/40 = (M x 7)/56 => M = 81

=> 81 – 45 = 36

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Q:

A and B together finish a wor in 20 days.They worked together for 15 days and then B left. Afer another 10 days,A finished the remaining work. In how many days A alone can finish the job?

A) 30	B) 40
C) 50	D) 60

Answer & Explanation Answer: B) 40

Explanation:

(A+B)'s 15 days work = $(\frac{1}{20} \times 15) = \frac{3}{4}$

Remaining work = 1/4

Now, 1/4 work is done by A in 10 days.

Whole work will be done by A in (10 x 4) = 40 days.

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Q:

A and B together can do a piece of work in 9 days. If A does thrice the work of B in a given time, the time A alone will take to finish the work is

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

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