Question

2 women and 5 men can together finish embroidery work in 4 days while 3 women and 6 men can finish in 5 days. Find the time taken by women alone to finish work and also taken by man alone.

Answer 1

Given:

• 2 women and 5 men can together finish embroidery work in 4 days
• 3 women and 6 men can finish in 5 days

To Find:

• Time taken by women alone to finish work and also taken by man alone.

Solution:

Let the number of days taken by a woman and a man be x and y

$\colon\implies$ 4(2/x + 5/y) = 1

$\colon\implies$ 2/x + 5/y = 1/4

$\colon\implies$ 3(3/x + 6/y) = 1

$\colon\implies$ 3/x + 6/y = 1/3

Putting 1/x = p and 1/y = q in Equations;

$\colon\implies$ 2p + 5q = 1/4

By cross multiplication,

$\colon\implies$ p/-20 – (-18) = q/-9 – (-18)

$\colon\implies$ 1/144b- 180 ⇒ p/-2

$\colon\implies$ q/-1 = 1/-36 ⇒ p/-2

$\colon\implies$– 1/36 and q/-1 = 1/-36

$\colon\implies$ p = 1/18 and q = 1/36

$\colon\implies$ p = 1/x = 1/18 and q = 1/y = 1/36

$\colon\implies$ x = 18 and y = 36

Hence,

• Number of days taken by a woman = 18 days
• Number of days taken by a man = 36 Days