# If 12 Men and 16 Boys Can Do a Piece of Work in 5 Days And, 13 Men and 24 Boys Can Do It in 4 Days, How Long Will 7 Men and 10 Boys Take to Do It? - Mathematics

Sum

If 12 men and 16 boys can do a piece of work in 5 days and, 13 men and 24 boys can do it in 4 days, how long will 7 men and 10 boys take to do it?

#### Solution

12 men + 16 boys can do a piece of work in = 5 days

60 men + 80 boys can do a piece of work in = 1 day ......…. (i)

and 13 men + 24 boys can do the same work in = 4 days

52 men + 96 boys can do the same work in = 1 day ………….(ii)

From (i) and (ii)

60 men + 80 boys = 52 men + 96 boys

⇒ 60 men – 52 men = 96 boys – 80 boys

⇒ 8 men = 16 boys

1 man =16/8 = boys

Now, in first case,

12 men + 16 boys = 12 x 2 + 16 = 24+16 = 40 boys

In the second case,

7 men + 10 boys = 7 x 2 + 10 = 14 + 10 = 24 boys

Now 40 boys can do a piece of work in = 5 days

1 boy can do the same work in = 5 x 40 days

and 24 boys will do the same work in
=(5xx40)/24 days

=25/3

=8 1/3 days

Concept: Concept for Unitary Method (With Only Direct Variation Implied)
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#### APPEARS IN

Selina Concise Mathematics Class 8 ICSE
Chapter 10 Direct and Inverse Variations
Exercise 10 (C) | Q 14 | Page 126