Time and Work Question 3 - CAT 2021
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:
A) 9000
B) 9200
C) 9100
D) 9150
Step-by-Step Explanation
Track the total number of days each individual contributed to the painting project:
- Anil worked from day 1 to day 24 = 24 days.
- Bimal joined later and worked for the final 14 days.
- Charu joined later and worked for the final 14 days.
- Calculate the exact fractions of the project completed by the two workers with known standalone timelines:
Fraction completed by Anil = 24 days/60 days = 2/5
Fraction completed by Bimal = 14 days/84 days = 1/6
The remainder of the work must have been completed by Charu:
Fraction completed by Charu
= 1 − (2/5 + 1/6)
= 1 − 17/30
= 13/30
Since workers are compensated in direct proportion to their total work output:
Charu's Share = 13/30 × ₹21,000
= 13 × 700
= ₹9,100
Correct Option: C
💡 FundaMakers Tip:
When multiple workers join a project at different times, do not compute arbitrary daily efficiency numbers for the entire group if individual deadlines are missing. Instead, calculate the standalone work fractions for the known workers. Subtracting these fractions from 1 gives the missing worker's contribution immediately.