CAT 2023 Slot 3 QA Question 14

Type-in-the-answer (no negative marking) · Arithmetic · Time & Work · Try it, then check the answer and solution below.

Gautam and Suhani, working together, can finish a job in 20 days. If Gautam does only

60 \%

of his usual work on a day, Suhani must do

150 \%

of her usual work on that day to exactly make up for it. Then, the number of days required by the faster worker to complete the job working alone is

TITA Answer:

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Official Convenor Answer Key: 36

Answer and solution

Answer: 36

📌 Core Concept & Formula

The combined work rate of two individuals working together is the sum of their individual work rates. If their combined work rate is

\frac{1}{T}

jobs per day, then:

\text{Gautam's rate} + \text{Suhani's rate} =

\frac{1}{T}

🔢 Step-by-Step Solution

Let Gautam's usual work rate be

G

jobs per day and Suhani's usual work rate be

S

jobs per day.

Given that together they finish the job in 20 days:

G + S = \frac{1}{20}

On a day when Gautam works at 60\% efficiency and Suhani works at 150\% efficiency:

0.6G + 1.5S = \frac{1}{20}

Express

G

from the first equation:

G = \frac{1}{20} - S

Substitute

G

into the second equation:

0.6\left(\frac{1}{20} - S\right) + 1.5S = \frac{1}{20}

Simplify the equation:

$ 0.03 - 0.6S + 1.5S = 0.05 0.03 + 0

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