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

Step 1: Work Rates 

Anil's work rate is $ \frac{1}{12} $ of the house per day (completes in 12 days).
Barun's work rate is $ \frac{1}{16} $ of the house per day (completes in 16 days).
When all three (Anil, Barun, Chandu) work together, they complete the house in 6 days, so their combined rate is $ \frac{1}{6} $ per day.

Step 2: Set up the equation

Let Chandu’s work rate be $ x $.
Then, according to the problem:
$ \frac{1}{12} + \frac{1}{16} + x = \frac{1}{6} $

Step 3: Solve for Chandu's rate

Take LCM of 12 and 16: LCM = 48
$ \frac{1}{12} = \frac{4}{48}, \quad \frac{1}{16} = \frac{3}{48}, \quad \frac{1}{6} = \frac{8}{48} $

So:
$ \frac{4}{48} + \frac{3}{48} + x = \frac{8}{48} $
$ \frac{7}{48} + x = \frac{8}{48} $
$ x = \frac{1}{48} $

Step 4: Chandu’s contribution in 6 days

In 6 days, Chandu completes:
$ 6 \times \frac{1}{48} = \frac{6}{48} = \frac{1}{8} $ of the house

Step 5: Chandu’s payment share

Total payment = ₹24000
Chandu's share = $ \frac{1}{8} \times 24000 = ₹3000 $

Final Answer: Chandu will receive ₹3000.