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 the total work be $W$ units.
Each person worked for 6 days.

Anil's work:
Anil completes the work in 12 days, so in 1 day, he does $\frac{1}{12}$ of the work.
In 6 days, he completes: \[ 6 \times \frac{1}{12} = \frac{6}{12} = \frac{1}{2} \Rightarrow \text{Anil's contribution} = \frac{W}{2} \]

Barun's work:
Barun completes the work in 16 days, so in 1 day, he does $\frac{1}{16}$ of the work.
In 6 days, he completes: \[ 6 \times \frac{1}{16} = \frac{6}{16} = \frac{3}{8} \Rightarrow \text{Barun's contribution} = \frac{3W}{8} \]

Total work done:
Together they completed the entire work $W$ in 6 days.
Let Charu’s contribution be $x$. Then, \[ \frac{W}{2} + \frac{3W}{8} + x = W \] Combine terms: \[ \frac{4W + 3W}{8} + x = W \Rightarrow \frac{7W}{8} + x = W \Rightarrow x = W - \frac{7W}{8} = \frac{W}{8} \]

Charu's share in money:
Total payment = ₹24,000
Charu’s share: \[ \frac{1}{8} \times 24000 = ₹3,000 \] Answer: ₹3,000

Answer 2

Given that Anil can paint a house in \(12\) days, and Barun can paint it in \(16\) days.
Now, Arun, Barun, and Chandu painted the house together in \(6\) days. 

Let the total work be \(W\), and each worked for \(6\) days.

Anil's work in 6 days = \( \frac{6}{12}W = \frac{1}{2}W \)
Barun's work in 6 days = \( \frac{6}{16}W = \frac{3}{8}W \)

Hence, Chandu's work = \( W - \left( \frac{1}{2}W + \frac{3}{8}W \right) = W - \frac{7}{8}W = \frac{1}{8}W \)

Therefore, Chandu's share of the money = \( \frac{1}{8} \times 24000 = \text{Rs. }3000 \)

Final Answer: \( \text{Rs. }3000 \)