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.

Answer 2

Given that, Anil can paint a house in \(12\) days while Barun can paint it in \(16\) days.
Now, Arun, Barun and Chandu painted  together in \(6\) Days.
Now, let total work be \(W\) and each worked for \(6\) days.
Then, Anil's work \(= 0.5W\)
Barun's work \(= \frac {6W}{16}\)= \(= \frac {3W}{8}\)
Hence, Charu's work = \(\frac W2- \frac {3W}{8} = \frac W8\)
Then the amount received by Chandu,
\(=\)\(\frac {24000}{8}\)
\(= Rs.\ 3000\)

So, the answer is \(Rs.\ 3000\).