Question

PLEASE ANSWER THIS QUESTION

Six men and eight women can do a piece of work in 15 days. Eleven men and sixteen women can do the same work in 8 days. In how many days can 4 men and 4 women do the work?

BRAINLIEST QUESTION

Answer 1

Let, 1 man can finish the work in a days

And 1 women can finish the work in b days

1 man's one day work = 1 /a

6 man's one day work = 6/a

1 women's one day work = 1/b

8 women's one day work = 8/b

( 6 man + 8 women)'s one day work = 6/a + 8/b

= ( 8a + 6b)/ ab

Number of days Required for 6 man and 8 woman to finish the work = ab / (8a + 6b)

=> ab / (8a + 6b) = 15

=> ab = 120a + 90b -------(1)

Similarly,

Number of days Required for 11 man and 16 woman to finish the work = ab / (16a + 11b)

=> ab / (16a + 11b) = 8

=> ab = 128a + 88b -------(2)

On comparing equation 1 and 2, we get

120a + 90b = 128a + 88b

=> 90b - 88b = 128a - 120a

=> 2b = 8a

=> b = 4a

Now,

On substituting the value b in equation 1, we get

a ( 4a) = 120a + 90 (4a)

=> 4a^2 = 120a + 360a

=> 4a^2 = 480a

=> a^2 = 120a

=> a = 120

b = 4 × 120 = 480

One men can finish the work in 120 days

One women can finish the work in 480 days

Now,

(4 men and 4 woman)'s one day work = 4/a + 4/b

= ( 4a + 4b)/(a b)

Number of days Required for 4 men and 4 women to finish the work = ab / ( 4a + 4b)

= 120 × 480 / ( 4 × 120 + 4 × 480)

= 120 × 480 / 4 × 120 ( 1 + 4)

= 480 / 4 × 5

= 120 /5

= 24

Required number of days = 24