# Formulate the following problems as a pair of equations, and hence find their solutions: 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 to finish the work, and also that taken by 1 man alone. - Mathematics

Formulate the following problems as a pair of equations, and hence find their solutions:

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 to finish the work, and also that taken by 1 man alone.

#### Solution

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

Therefore, work done by a woman in 1 day = 1/x

According to the question,

4(2/x + 5/y) = 1

2/x + 5/y = 1/4

3(3/x + 6/y) = 1

3/x + 6/y = 1/3

Putting 1/x = p  in these equations, we get

2p + 5q = 1/4

By cross multiplication, we get

p/(-20-(-18)) = q/(-9-(-18)) = 1/(144-180)

p/-2 = q/-1 = 1/-36

p/-2 = -1/36

p = 1/18

p = 1/x = 1/18

x = 18 and y = 36

Hence, number of days taken by a woman = 18 and number of days taken by a man = 36

Concept: Equations Reducible to a Pair of Linear Equations in Two Variables
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#### APPEARS IN

NCERT Class 10 Maths
Chapter 3 Pair of Linear Equations in Two Variables
Exercise 3.6 | Q 2.2 | Page 67