Q. 214.1( 9 Votes )

# 2 men and 7 boys can do a piece of work in 4 days. The same work is done in 3 days by 4 men and 4 boys. How long would it take one man and one boy to do it?

Answer :

**To find:** Time taken by one boy and 1 man.

**Explanation:**

Let the number of days in which 1 man and 1 boy can do the work be ‘a’ and ‘b’ respectively.

In 1 day,

In a days 1 man can work

⇒ In 1 day 1/a man can do work

⇒ 2 men can do work in 2/a days.

Similarly

In b days 1 boy can work

⇒ In 1 day 1/b boy can do work

⇒ 7 boys can do work in 7/b days

Given, 2 men and 7 boys can do a piece of work in 4 days. The same work is done in 3 days by 4 men and 4 boys.

Multiplying eq1 by 2 and subtracting eq2 from eq1

⇒ b = 60 days

Substitute the value of b in eq.2 to get,

⇒ a = 15 days

**Thus 1 man can do work in 15 days and 1 boy can do work in 60 days.**

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Solve the following pair of linear equation by cross - multiplication method:

x + 4y + 9 = 0

5x – 1 = 3y

KC Sinha - Mathematics