(Q14).Formulate the following problems as a pair of equations and then find their solutions.

(iii) 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.

Let the time taken by 1 woman to complete the work = x days

and time taken by 1 man to complete the work = y days

∴ Work done by 1 woman in 1 day =
1
x
∴ Work done by 1 man in 1 day =
1
y

By problem,

(
x
 +
y
 ) = 1 and (
x
 +
y
 ) = 1
⇒
x
 +
y
 =
1
 and
x
 +
y
 =
1
Take
1
x
 = and
1
y
 = ,

then the above equations reduce to

a + b =
1
 and a + b =
1

⇒ a + b = 1 …….. (1) and

a + b = 1 ……… (2)

equation (1) × ⇒ a + b =
equation (2) × ⇒ a + b =
(-) b =
⇒ b =
Substituting b =
1
 in equation (1) we get
8a + 20 (
1
 ) = 1
⇒ 8a = 1 -
⇒ 8a =
⇒ a =
× 8
=
1
but a =
1
x
 =
1
 ⇒ x = and
b =
1
y
 =
1
 ⇒ y =

∴ Time taken by 1 woman = days

1 man = days