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CAT 2021 Slot 3 — QA Question 7

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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 & solution

Answer: 3000

Solution

Easy

Payment is split in proportion to work done. Find what fraction of the house Chandu painted: subtract Anil's and Barun's shares (over 66 days) from the whole. That fraction of ₹24000\textsf{₹}24000 is Chandu's pay.

1

Fractions done by Anil and Barun in 66 days. Anil finishes in 1212 days, Barun in 1616 days, so per day they do 112\tfrac1{12} and 116\tfrac1{16}.

Anil=612=12Barun=616=38\begin{aligned} &\text{Anil}=\frac{6}{12}=\frac12\\ &\text{Barun}=\frac{6}{16}=\frac38 \end{aligned}
2

Chandu's share of the work. The three together complete the whole house, so Chandu's fraction is the remainder.

Chandu=1−12−38(from step 1)⇒ =8−4−38=18\begin{aligned} &\text{Chandu}=1-\frac12-\frac38 \quad\text{(from step 1)}\\ &\Rightarrow\ =\frac{8-4-3}{8}=\frac18 \end{aligned}
3

Chandu's payment. Pay is proportional to work, so Chandu receives 18\tfrac18 of ₹24000\textsf{₹}24000.

Pay=18×24000=3000\begin{aligned} &\text{Pay}=\frac18\times 24000=3000 \end{aligned}
Chandu receives=₹ 3000\text{Chandu receives}=\textsf{₹}\,3000
CAT 2021 Slot 3 QA Q7: Anil can paint a house in 12 days while Barun can paint it in 16 days. Anil, Barun, and Chandu undertake to pa — Solution | TheCATExam