**Time and Work**

**13.)** Women can complete a work in 7 days and 10 children take 14 days to complete the work. How many days will 5 women and 10 children take to complete the work?

**A.** 3 **B.** 5

**C.** 7 **D.** cannot be determined

**View Answer**

**Answer:**Option

**C**

Explanation:

1 woman's 1 day's work = 1/70

1 child's 1 day's work = 1/140

(5 women + 10 children)'s day's work = ( 5/70 + 10/140) = 1/14 + 1/14=1/7

5 women and 10 children will complete the work in **7 days.**

**14.)**X and Y can do a piece of work in 20 days and 12 days respectively. X started the work alone and then after 4 days Y joined him till the completion of the work. How long did the work last?

**A.** 6 days **B. ** 10 days

**C.** 15 days ** D. ** 20 days

**View Answer**

**Answer:**Option

**B**

Explanation:

Work done by X in 4 days = (1/20x 4) = 1/5

Remaining work = 1 - 1/5 = 4/5

(X + Y)'s 1 day's work = 1/20 + 1/12) = 8/60 = 2/15

Now, 2/15 work is done by X and Y in 1 day.

So, 4/5 work will be done by X and Y in (15/2 x 4/5) = 6 days.

Hence, total time taken = (6 + 4) days = **10 days.**

**15.)**Ravi and Kumar are working on an assignment. Ravi takes 6 hours to type 32 pages on a computer, while Kumar takes 5 hours to type 40 pages. How much time will they take, working together on two different computers to type an assignment of 110 pages?

**A.** 7 hours 30 minutes **B. ** 8 hours

**C. ** 8 hours 15 minutes **D. ** 8 hours 25 minutes

**View Answer**

**Answer:**Option

**C**

Explanation:

Number of pages typed by Ravi in 1 hour = 32/6 = 16/3

Number of pages typed by Kumar in 1 hour = 40/5 = 8.

Number of pages typed by both in 1 hour = (16/3 + 8) = 40/3

.*. Time taken by both to type 110 pages = (110 x 3/40) hours

= 8 ¼ hour (or) **8 hours 15 minutes.**

16.) Twenty women can do a work in sixteen days. Sixteen men can complete the same work in fifteen days. What is the ratio between the capacity of a man and a woman?

**A. ** 3: 4 **B. ** 4: 3

**C.** 5: 3 **D.** Data inadequate

**View Answer**

**Answer:**Option

**B**

Explanation:

(20 x 16) women can complete the work in 1 day.

1 woman's 1 day's work = 1/320

(16 x 15) men can complete the work in 1 day.

1 man's 1 day's work = 1/240

So, required ratio = 1/240: 1/320

= 1/3: 1/4

= 4: 3 (cross multiplied)

**17.)**A works twice as fast as B. If B can complete a work in 12 days independently, the number of days in which A and B can together finish the work in:

**A. ** 4 days ** B. ** 6 days

**C. ** 8 days ** D. ** 18 days

**View Answer**

**Answer:**Option

**A**

Explanation:

Ratio of rates of working of A and B = 2: 1.

So, ratio of times taken = 1: 2.

B's 1 day's work = 1/12

A's 1 day's work = 1; (2/6 times of B's work)

(A + B)'s 1 day's work = (1/6 + 1/12) = 3/12 = 1/4

So, A and B together can finish the work in 4 days.