Formulate the following problems as a pair of equation and then find their solution.
2 women and 5 men can together finish an embroidery work in 4 days while 3 women and 6 men can finish it in 3 days. Find the time taken by 1 woman alone and 1 man alone to finish the work.

Question

Philoid · Accepted Answer

Let the time taken by one woman to finish the work = x days

Work done by one women in one day = days

Let the time taken by one man to finish the work = y days

Work done by one men in one day = days

Now, 2 women and 5 men can finish the work in 4 days

So, ⇒ …I

Also, 3 women and 6 men can finish the work in 3 days

So, ⇒ …II

Let be a and be b

8a + 20b = 1 …III

9a + 18b = 1 …IV

Multiplying Eq. III by 9 and Eq. IV by 8 and solving

72a + 180b = 9

72a + 144b = 8

_- - - _

36b = 1

b =

substituting value of b in Eq. III

8a + 20 × = 1

288a + 20 = 36

288a = 16

a =

⇒ x = 18

⇒ y = 36

Number of days by man = 18;

Number of days by woman = 36

Formulate the following problems as a pair of equation and then find their solution.2 women and 5 men can together finish an embroidery work in 4 days while 3 women and 6 men can finish it in 3 days. Find the time taken by 1 woman alone and 1 man alone to finish the work.