Question

73. 12 men or 15 women can finish a
work in 24 days. In how many days
the same work can be finished by 8
men and 8 women?
(1 )16 days (2) 20 days
(3) 24 days (4) 28 days​

Answer 1

Answer:

12 men or 15 women can finish a work in 24 days, in how many days can the same work be finished by 8 men and 8 women?

Work and Time problems can be solved using ratios . The basic formula used is:

M1 × D1 / W1 = M2 × D2 / W2 —————— (1)

Where M1 is number of people required for doing work W1 in D1 time and M2 is the number of people required for doing work W2 in D2 time.

The time required for completing the work by 12 Men is the same as that for 15 women

12M = 15 W

4 M = 5 W

M = 5/4 W ————————— (2)

From the given scenario substitute values in equation (1)

(8M + 8 W ) × D = 15 W × 24 ————— (3)

Where D is the number of days required to complete the work in 8 men and 8 women

From equation (2) substitute M = 5/4 W in equation (3)

(8×5/4 W + 8 W)×D =15 W ×24

(10 W + 8 W )× D = 15 W × 24

18 × D = 15 × 24

D = 20

The time required for 8 men and 8 women is 20 days.

Answer 2

Answer:

2) 20 days

12 men's do a work in 24 days,

So, work done by 12 men's in 1 day will be 1/24

So, work done by 1 men in 1 day will be 1/24×1/12.i.e. 1/288

similarly same work done by women in 1 day will be 1/24×1/15. i.e.1/360

8/288+8/360

1/36+1/45=5/180+4/180

9/180=1/20

This is the work done in 1 day by 8 men's and 8 women's together

Therefore they take 20 days to complete the work.