420+ Solved Time and Work Problems with Solutions and Explanation

Q:

Kaushalya can do a work in 20 days, while kaikeyi can do the same work in 25 days. They started the work jointly.Few days later Sumitra also joined them and thus all of them completed the whole work in 10 days. All of them were paid total Rs.700. What is the Share of Sumitra?

A) Rs.130	B) Rs.185
C) Rs.70	D) can't be determined

Answer & Explanation Answer: C) Rs.70

Explanation:

Efficiency of kaushalya = 5%

Efficiency of kaikeyi = 4%

Thus, in 10 days working together they will complete only 90% of the work.

[(5+4)*10] =90

Hence, the remaining work will surely done by sumitra, which is 10%.

Thus, sumitra will get 10% of Rs. 700, which is Rs.70

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12 14889

Q:

Two pipes A and B can fill a cistern in 4 minutes and 6 minutes respectively . If these pipes are turned on alternately for 1 minute each how long will it take to the cistern to fill?

Answer

As the pipes are operating alternatively, thus their 2 minutes job is = $\frac{1}{4} + \frac{1}{6} = \frac{5}{12}$

In the next 2 minutes the pipes can fill another $\frac{5}{12}$ part of cistern.

Therefore, In 4 minutes the two pipes which are operating alternatively will fill $\frac{5}{12} + \frac{5}{12} = \frac{5}{6}$ Remaining part = $1 - \frac{5}{6} = \frac{1}{6}$

Pipe A can fill $\frac{1}{4}$ of the cistern in 1 minute

Pipe A can fill $\frac{1}{6}$ of the cistern in = $\frac{2}{3}$ min

Therefore, Total time taken to fill the Cistern

4 + $\frac{2}{3}$ minutes.

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28 14676

Q:

12 men complete a work in 9 days. After they have worked for 6 days, 4 more men join them. How many days will they take to complete the remaining work ?

A) 2 days	B) 2.5 days
C) 2.25 days	D) 3 days

Answer & Explanation Answer: C) 2.25 days

Explanation:

1 man's 1 day work = 1/108
12 men's 6 day's work = 1/9 x 6 = 2/3

Remaining work = 1 - 2/3 = 1/3

16 men's 1 day work = 1/108 x 16 = 4/27
4/27 work is done by them in 1 day.

1/3 work is done by them in 27/4 x 1/3 = 9/4 days.

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18 14666

Q:

P, Q, and R can do a job in 12 days together. If their efficiency of working be in the ratio 3 : 8 : 5, Find in what time Q can complete the same work alone?

A) 36 days	B) 30 days
C) 24 days	D) 22 days

Answer & Explanation Answer: A) 36 days

Explanation:

Given the ratio of efficiencies of P, Q & R are 3 : 8 : 5

Let the efficiencies of P, Q & R be 3x, 8x and 5x respectively

They can do work for 12 days.

=> Total work = 12 x 16x = 192x

Now, the required time taken by Q to complete the job alone = $\frac{162 x}{8 x} = 24$ days.

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17 14573

Q:

If 34 men completed 2/5th of a work in 8 days working 9 hours a day. How many more man should be engaged to finish the rest of the work in 6 days working 9 hours a day ?

A) 101 men	B) 112 men
C) 102 men	D) 120 men

Answer & Explanation Answer: C) 102 men

Explanation:

From the above formula i.e (m1 x t1/w1) = (m2 x t2/w2)

so, [(34 x 8 x 9)/(2/5)] = [(M x 6 x 9)/(3/5)]

so, M = 136 men

Number of men to be added to finish the work = 136-34 = 102 men.

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14 14569

Q:

Time taken by P alone to finish a work is 50% more than the time taken by P and Q together. Q is thrice as efficient as R. If Q and R together can complete the work in 22.5 days, then how many days will P alone take to complete the work ?

A) 17 days	B) 11 days
C) 15 days	D) 16 days

Answer & Explanation Answer: C) 15 days

Explanation:

We know that Time is inversely proportional to Efficiency

Here given time ratio of P & P+Q as

P/P+Q = 150/100 = 3:2

Efficiency ratio of P & Q as

P:Q = 2:1 ....(1)

Given Efficiency ratio of Q & R as

Q:R = 3:1 ....(2)

From (1) & (2), we get

P:Q:R = 6:3:1

P alone can finish the work in

22.5(3+1)/6 = 15 days.

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18 14356

Q:

If 5 men and 2 boys working together, can do four times as much work per hour as a man and a boy together. Find the ratio of the work done by a man and that of a boy for a given time ?

A) 1:2	B) 1:3
C) 3:1	D) 2:1

Answer & Explanation Answer: D) 2:1

Explanation:

5M + 2B = 4(1M + 1B)

5M + 2B = 4M + 4B

1M = 2B

The required ratio of work done by a man and a boy = 2:1

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8 14318

Q:

A can write 32 pages in 6 hours and B can write 40 pages in 5 hours. If they write together, in how many hours they can write 110 pages ?

A) 7 hrs	B) 6 hrs 10 min
C) 5 hrs 25min	D) 8 hrs 15 min

Answer & Explanation Answer: D) 8 hrs 15 min

Explanation:

A can write in 1hour = 32/6 pages

Similarly, B in 1 hour = 40/5 pages

Together (A+B) in 1 hour = 32/6 + 40/5 = 40/3

So, A+B write 40/3 pages in 1 hour

A+B write 110 pages in (3/40) x 110 Hours = 8 hours 15 min.

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