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

Correct Answer: 3000

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.