Explanation:

Let’s break it down step by step:

- 4 men + 6 boys finish the work in 8 days. That means (4M + 6B) × 8 = 1 work unit.

- 6 men + 4 boys finish in 7 days. So (6M + 4B) × 7 = 1 work unit.

Let's turn these into equations for “work per day”:

- 4M + 6B = 1/8

- 6M + 4B = 1/7

Now multiply both out to clear fractions:

- 4M + 6B = 0.125

- 6M + 4B = 0.142857

Let’s solve:

- Multiply the first by 3: 12M + 18B = 3/8 = 0.375

- Multiply the second by 2: 12M + 8B = 2/7 = 0.28571

Subtract the second from the first:

- (12M + 18B) - (12M + 8B) = 0.375 - 0.28571

- 10B = 0.08929 ? B = 0.008929

Plug B back into the first equation:

- 4M + 6 × 0.008929 = 0.125

- 4M + 0.05357 = 0.125

- 4M = 0.07143 ? M = 0.017857

Now, what about 5 men and 4 boys?

- 5 × 0.017857 + 4 × 0.008929 = 0.089285 + 0.035714 = 0.125

That means 5 men and 4 boys do 0.125 (or 1/8) of the work per day. So, they will do the work in 8 days.

Here’s what that means for the options:

- Option 1, 5 days: Too fast.

- Option 2, 8 days: Spot on.

- Option 3, 6 days: Not matching the numbers.

- Option 4, 7 days: Still not matching.