The wages of 3 boys are equal to the wages of 2 men. The amount of work done by 3 men is equal to the amount of work done by 5 boys. If 40 boys and 15 men worked for 8 weeks to complete a work and the total wages they got are equal to Rs.12,600 then the wages 20 boys and 20 men get to complete that work is (in rupees)

Given:

The wages of 3 boys are equal to the wages of 2 men.

The amount of work done by 3 men is equal to the amount of work done by 5 boys.

40 boys and 15 men worked for 8 weeks, and their total wages = ₹12,600.

We need to find the wages of 20 boys and 20 men to complete the same work.

Formula used:

1. Ratio of wages of boys to men = \(\frac{\text{Work done by boys}}{\text{Work done by men}}\)

2. Total wages = Sum of wages for all boys and men.

Calculation:

From the question:

The work done by 3 men = Work done by 5 boys.

⇒ Work done by 1 man = Work done by \(\frac{5}{3}\) boys.

Also, wages of 3 boys = Wages of 2 men.

⇒ Wages of 1 boy = Wages of \(\frac{2}{3}\) men.

Let the wages of 1 man per week = ₹m and 1 boy per week = ₹b.

From wages ratio: \(\frac{b}{m} = \frac{2}{3}\)

⇒ b = \(\frac{2}{3}m\)

Now, total wages for 40 boys and 15 men for 8 weeks = ₹12,600.

⇒ 8 weeks × (40 boys × b + 15 men × m) = ₹12,600

⇒ 8 × (40 × \(\frac{2}{3}m\) + 15 × m) = ₹12,600

⇒ 8 × (\(\frac{80m}{3} + 15m\)) = ₹12,600

⇒ \(\frac{8(80m + 45m)}{3} = 12,600\)

⇒ \(\frac{8 × 125m}{3} = 12,600\)

⇒ \(\frac{1000m}{3} = 12,600\)

⇒ \(\frac{m}{3} = 12.6\)

⇒ m = ₹37.8

⇒ b = \(\frac{2}{3} × 37.8 = ₹25.2\)

Now, calculate wages for 20 boys and 20 men:

Total wages = (20 boys × b × 8 weeks) + (20 men × m × 8 weeks)

⇒ Total wages = (20 × 25.2 × 8) + (20 × 37.8 × 8)

⇒ Total wages = (4032) + (6048)

⇒ Total wages = ₹10,080

∴ The correct answer is ₹10,080.