Question

Anil can paint a house in 12 days while Barun can paint it in 16 days. Anil, Barun, and Chandu undertake to paint the house for ₹ 24000 and the three of them together complete the painting in 6 days. If Chandu is paid in proportion to the work done by him, then the amount in INR received by him is

Answer 1

Let's first determine the work rates for Anil and Barun.

Anil's work rate is $\frac{1}{12}$ of the house per day since he can complete painting the house in 12 days.
Similarly, Barun's work rate is $\frac{1}{16}$ of the house per day. When Anil, Barun, and Chandu work together, they complete the house in 6 days.

So, their combined work rate is $\frac{1}{6}$ of the house per day.

Given the work rates for Anil and Barun:
$Anil + Barun + Chandu = \frac{1}{6}$

Substituting in the known rates:
$\frac{1}{12} + \frac{1}{16} + Chandu = \frac{1}{6}$

Finding the least common denominator, which is 48: $4 + 3 + 48 \times Chandu = 8$
$48 \times Chandu = 1$
$Chandu = \frac{1}{48}$

This means Chandu's work rate is $\frac{1}{48}$ of the house per day.

Over 6 days, Chandu would have completed:

$6 \times \frac{1}{48} = \frac{1}{8}$ or 12.5% of the house.

So, Chandu's share of the payment is 12.5% of ₹24000:
$0.125 \times 24000 = ₹3000$
So, Chandu will receive ₹3000.