Question

If 9 men and 12 boys can do a piece of work in 4 days and 4 men and 16 boys can do the same piece of work in 6 days, how long will 6 men and 24 boys take to complete the same work?

(A) 3 days

(C) 5 days

W-0017

(B) 4 days

(D) 6 days​

Answer 1

Heya!!

Here's your answer!!

Let us take a man use to complete a part of work in a single day : M

A boy use to complete a part of work in a single day : B

As per first statement 9 men and 12 boys can complete a piece of work in 4 days.

Therefore, 4M + 12 B = 4 days ..... ..... ..... (1)

By second statement 4 men and 16 boys altogether complete the same work in 6 days.

Therefore, 4M + 16 B = 6 days .... ..... ..... (2)

From (1) and (2) we get

9 M + 12 B = 4 days .... .... .... (1)

4 M + 16 B = 6 days .... ..... ..... (2)

Just multiply days what man and boy and make them equal as work remains the same.

(9 × 4)M + (12 × 4)B = (4 × 6)M + (16 × 6)B

Now bring man one side and boy to another

36 M - 24 M = 96 B - 48 B

12 M = 48 B

1M = 4B .... ..... .... (3)

Now substitute M value in 9 M + 12 B = 4 days. ... ... ... (1)

we get,

9 × 4 B + 12B = 4

36 B + 12 B = 4

48 B = 4

B = 1/12 ... ... ... (4)

Now substitute B value in (3) i.e., 1M = 4B

M = 4 × 1/12

we get : M = 1/3 .... ... .... (5)

As per last statement

6 men and 24 boys can complete in :

Now put (4) and (5) value in

6 M + 24 B we get,

6 × 1/3 + 24 × 1/12

6/3 + 24/12

2+2

4 days.

Glad help you,

It helps you,

thanks.