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CAT 2021 Slot 2 — QA Question 4

PaymentsEasy

Anil can paint a house in 60 days while Bimal can paint it in 84 days. Anil starts painting and after 10 days, Bimal and Charu join him. Together, they complete the painting in 14 more days. If they are paid a total of ₹ 21000 for the job, then the share of Charu, in INR, proportionate to the work done by him, is 

Answer & solution

  • 9100

  • B

    9000

  • C

    9150

  • D

    9200

Solution

Easy

Take total work as the LCM of the times so daily rates are whole numbers. Compute Anil's and Bimal's contributions; whatever work is left was done by Charu, and the pay splits in the same ratio as work.

1

Fix total work and rates. Let total work =lcm⁡(60,84)=420=\operatorname{lcm}(60,84)=420 units.

Anil=42060=7 units/dayBimal=42084=5 units/day\begin{aligned} &\text{Anil}=\tfrac{420}{60}=7\ \text{units/day}\\ &\text{Bimal}=\tfrac{420}{84}=5\ \text{units/day} \end{aligned}
2

Track the timeline. Anil works alone for 1010 days, then all three work 1414 more days, so Anil works 2424 days and Bimal works 1414 days.

Anil’s work=24×7=168Bimal’s work=14×5=70\begin{aligned} &\text{Anil's work}=24\times 7=168\\ &\text{Bimal's work}=14\times 5=70 \end{aligned}
3

Charu's work is the remainder. The job finishes (420420 units done).

Charu=420−168−70=182 units\begin{aligned} &\text{Charu}=420-168-70=182\ \text{units} \end{aligned}
4

Pay in proportion to work. Charu's share is 182420\tfrac{182}{420} of ₹2100021000.

Charu’s share=182420×21000⇒ =182×50=₹9100\begin{aligned} &\text{Charu's share}=\tfrac{182}{420}\times 21000\\ &\Rightarrow\ =182\times 50=\text{₹}9100 \end{aligned}
Charu’s share=₹9100\text{Charu's share}=\text{₹}9100
CAT 2021 Slot 2 QA Q4: Anil can paint a house in 60 days while Bimal can paint it in 84 days. Anil starts painting and after 10 days, — Solution | TheCATExam