CAT 2021 Slot 3 · Quant · Question 9

CAT 2021 Slot 3 previous year question on Time and Work, with the answer and a step-by-step solution.

Time and WorkArithmeticMultiple choiceMedium

One day, Rahul started a work at 9 AM and Gautam joined him two hours later. They then worked together and completed the work at 5 PM the same day. If both had started at 9 AM and worked together, the work would have been completed 30 minutes earlier. Working alone, the time Rahul would have taken, in hours, to complete the work is

A
12
B
11.5
C
12.5
D
10

Pick an option, then check.

Answer & solution

Answer: Option D

Let Rahul and Gautam do R and G of the work per hour.

What actually happened: Rahul worked 9 AM to 5 PM, which is 8 hours, and Gautam worked 11 AM to 5 PM, which is 6 hours. So 8R+6G=1.

The alternative: both work from 9 AM and finish at 4:30 PM, which is 7.5 hours each. So 7.5R+7.5G=1, giving R+G=\frac{2}{15}.

Substituting G=\frac{2}{15}-R into the first equation: 8R+6\left( \frac{2}{15}-R \right)=1, so 2R+\frac{4}{5}=1 and R=\frac{1}{10}.

Rahul alone therefore needs 10 hours.

CAT 2021 Slot 3 · Quant · Question 9

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