Aptitude - Time and Work

Each of the questions given below consists of a question followed by three statements. You have to study the question and the statements and decide which of the statement(s) is/are necessary to answer the question.

1. 

In how many days can 10 women finish a work?

I. 

10 men can complete the work in 6 days.

II. 

10 men and 10 women together can complete the work in 3 3 days
7

 III. 

If 10 men work for 3 days and thereafter 10 women replace them, the remaining work in completed in 4 days.

A. Any two of the three
B. I and II only
C. II and III only
D. I and III only
E. None of these

Answer: Option A

Explanation:

  I. (10 x 6) men can complete the work in 1 day.

      1 man's 1 day's work = 1
60


 II. 10 x 24 men + 10 x 24 women can complete the work in 1 day.
7 7

      240 men's 1 day work + 240 women's 1 day work = 1.
7 7

      240 x 1 + 240 women's 1 day's work = 1.
7 60 7

      240 women's 1 day's work = 1 - 4 = 3
7 7 7

      10 women's 1 day's work = 3 x 7 x 10 = 1
7 240 8

      So, 10 women can finish the work in 8 days.


III. (10 men's work for 3 days) + (10 women's work for 4 days) = 1

      (10 x 3) men's 1 day's work + (10 x 4) women's 1 day's work = 1

      30 men's 1 day's work + 40 women's 1 day's work = 1


      Thus, I and III will give us the answer.

      And, II and III will give us the answer.

      Correct answer is (A).


2. 

How many workers are required for completing the construction work in 10 days?

I. 

20% of the work can be completed by 8 workers in 8 days.

II. 

20 workers can complete the work in 16 days.

 III. 

One-eighth of the work can be completed by 8 workers in 5 days.

A. I only
B. II and III only
C. III only
D. I and III only
E. Any one of the three

Answer: Option E

Explanation:

  I. 20 work can be completed by (8 x 8) workers in 1 day.
100

   Whole work can be completed by (8 x 8 x 5) workers in 1 day.

        = 8 x 8 x 5 workers in 10 days = 32 workers in 10 days.
10


 II. (20 x 16) workers can finish it in 1 day.

   (20 x 16) workers can finish it in 10 days.
10

   32 workers can finish it in 10 days.


III. 1 work can be completed by (8 x 5) workers in 1 day.
8

   Whole work can be completed by (8 x 5 x 8) workers in 1 day.

        = 8 x 5 x 8 workers in 10 days = 32 workers in 10 days.
10

Any one of the three gives the answer.

Correct answer is (E).