Question

If the work done by 8 men and 4 boys in 1 day is 7 times the work done by 1 man and 1 boy, then compare the work done by 1 man and 1 boy in 1 day.

• A. 1
• B. 2
• C. 3
• D. $\dfrac{1}{2}$

Hint:

Use variables for each worker’s rate and convert the comparison into a linear equation to simplify.

Answer 1

The Correct Option is C

Let work done by 1 man in 1 day be $M$ and by 1 boy be $B$.
So, work by 8 men and 4 boys = $8M + 4B$
Work by 1 man and 1 boy = $M + B$
Given: $8M + 4B = 7(M + B)$
Expand RHS: $8M + 4B = 7M + 7B$
Rearrange: $8M - 7M = 7B - 4B$
$M = 3B$
Now, $M + B = 3B + B = 4B$
So, $8M + 4B = 8(3B) + 4B = 24B + 4B = 28B$
Compare: $28B : 4B = 7 : 1$
Hence, ratio = $\boxed{3}$