420+ Solved Time and Work Problems with Solutions and Explanation

Q:

In a hostel, there was food for 1000 students for one month. After 10 days, 1000 more students joined the hostel. How long would the students be able to carry on with the remaining food?

A) 10 days	B) 15 days
C) 20 days	D) 5 days

Answer & Explanation Answer: A) 10 days

Explanation:

After 10 days, the remaining food would be sufficient for the 1000 students for 20 more days

-->If 1000 more students are added, it shall be sufficient for only 10 days (as the no. of students is doubled, the days are halved).

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Q:

A is 50% more efficient than B. They together start the work and 7/12th of work is left after 8 days. Find in what time B alone will complete the whole work.

A) 36 days	B) 44 days
C) 50 days	D) 40 days

Answer & Explanation Answer:

Explanation:

Ratio of efficiency of A to B is 3 : 2

Let, In 8 days they complete = (3 + 2) × 8 = 40 units

So, total work = 40 × 12/5 units

Time taken by B alone to complete whole work = 40 × 12/5 ×2 = 48 days

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5 8229

Q:

Ten women can do a work in six days. Six men can complete the same work in five days. What is the ratio between the capacity of a man and a woman?

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

Answer & Explanation Answer: B) 2:1

Explanation:

(10 * 6) women can complete the work in 1 day.

Therefore, 1 woman's 1 day's work = 1/60

(6 * 5) men can complete the work in 1 day.

Therefore, 1 man's 1 day's work = 1/30

so, required ratio =1/30 : 1/60 = 2:1

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Q:

At Arihant Prakasham every book goes hrough 3 phases (or stages) typing, composing and binding. There are 16 typists, 10 composers and 15 binders. A typist can type 8 books in each hour, a composer can compose 12 books in each hour and a binder can bind 12 books in each hour. All of the people at Arihant Prakasham works for 10 hours a day and each person is trained to do only the ob of 1 category.How many books can be prepared in each day?

A) 1500	B) 1200
C) 1440	D) 1380

Answer & Explanation Answer: B) 1200

Explanation:

T C B

16 10 15

8 12 12

128 120 180 <------- in one hour

1280 1200 1800 <------- in 10 hours

Since, restriction is imposed by composers i.e,since only 1200 books can be composed i 10 hours so not more than 1200 books can be finally pepared.

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Q:

A take twice as much time as B or thrice as much time to finish a piece of work. Working together, they can finish the work in 2 days. B can do the work alone in ?

A) 3 hrs	B) 6 hrs
C) 7 hrs	D) 5 hrs

Answer & Explanation Answer: B) 6 hrs

Explanation:

Suppose A, B and C take x, x/2 and x/3 respectively to finish the work.
Then, (1/x + 2/x + 3/x) = 1/2
6/x = 1/2 => x = 12
So, B takes 6 hours to finish the work.

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5 7773

Q:

P and Q can do a work in 4 hours and 12 hours respectively. P starts the work at 9am and they work alternately for one hour each. When will the work be completed ?

A) 3 am	B) 12 pm
C) 1 pm	D) 3 pm

Answer & Explanation Answer: D) 3 pm

Explanation:

Work done by P and Q in the first two hours, working alternately

= First hour P + Second hour Q

$\Rightarrow \frac{1}{4} + \frac{1}{12} = \frac{1}{3}$

work is completed in 2 hours

Then, the total time required to complete the work by P and Q working alternately=2 x 3= 6hours

Thus, work will be completed at 3pm.

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Q:

A laborer is engaged for 30 days on the condition that he receives Rs.25 for each day he works and is fined Rs.7.50 for each day is absent. He gets Rs.425 in all. For how many days was he absent ?

A) 10 days	B) 14 days
C) 11 days	D) 9 days

Answer & Explanation Answer: A) 10 days

Explanation:

For 30 days he receives

30 x 25 = 750

Actually he gets 425

Therefore, Fine is 750 - 425 = 325

=> No of days absent = 325/(25+7.50)= 10

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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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