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 $Rs.\ 3000$.