Question

5 men and 3 boys can do work in 40 days while 6 men and 2 boys can do this work in 36 days. Then, how many much time will be taken by 4 men and 4 boys to complete work?
1. 45 days
2. 40 days
3. 35 days
4. 55 days
5. 36 days

Answer 1

Correct Answer - Option 1 : 45 days

Given:

5 men and 3 boys can do work in 40 days

6 men and 2 boys can do this work in 36 days

Calculation:

According to the question:

(5M + 3B) × 40 = (6M + 2B) × 36

⇒ 50M + 30B = 54M + 18B

⇒ 50M – 54M = 18B – 30B

⇒ 12B = 4M

⇒ 1M = 3B

Now, (5M + 3B) = 5 × 3B + 3B

⇒ 15B + 3B = 18B

Again,

(4M + 4B) = 4 × 3B + 4B

⇒ 12B + 4B = 16B

18 boys take time 40 days.

1 boys take time = (40 × 1) days

16 boys take time = (40 × 18)/16 = 45 days

∴ 4 men and 4 boys to complete work in 45 days.