CAT 2023 Slot 3 QA Question 9

Multiple choice (+3 / −1) · Arithmetic · Time & Work · Try it, then check the answer and solution below.

CAT 2023 Slot 3QAArithmetic • Time & WorkHard

Rahul, Rakshita and Gurmeet, working together, would have taken more than 7 days to finish a job. On the other hand, Rahul and Gurmeet, working together would have taken less than 15 days to finish the job. However, they all worked together for 6 days, followed by Rakshita, who worked alone for 3 more days to finish the job. If Rakshita had worked alone on the job then the number of days she would have taken to finish the job, cannot

Practice More Questions

⌨️ Shortcuts:[1-4 / A-D] Select[Enter] Check[B] Star[S] Solution

Official Convenor Answer Key: C

Answer and solution

Answer: C) $21$

📌 Core Concept & Formula

The problem involves work rates and can be solved using the concept of combined work rates. If individuals have work rates

R , S , and

G , their combined work rate is

R + S + G

. The total work done is 1 job, so the time taken is the reciprocal of the combined work rate.

🔢 Step-by-Step Derivation

Define Variables:

Let

R , S , and

G$ be the work rates of Rahul, Rakshita, and Gurmeet respectively (in jobs per day).

Given Conditions:

All three together take more than 7 days:

R + S + G < \frac{1}{7}

Rahul and Gurmeet together take less than 15 days:

R + G > \frac{1}{15}

Work done:

6(R + S + G) + 3S = 1

Express

R + G

a

From the second condition:

a > \frac{1}{15}

Substitute into the Work Equation:

6(a + S) + 3S = 1

leads to

6a + 9S = 1

Solving for

a

a = \frac{1 - 9S}{6}

Inequality for

S

From

S < \frac{1}{7} - a , substitute

a$:

S < \frac{1}{7} - \frac{1 - 9S}{6}

Solving this gives

S > \frac{1}{21}

Determine Rakshita's Time:

S > \frac{1}{21} implies \frac{1}{S} < 21

Thus, Rakshita cannot take 21 days.

⚡ 30-Second Shortcut

From the inequalities, derive that

S > \frac{1}{21} , so the time \frac{1}{S}

must be less than 21 days. Hence, 21 days is impossible

CAT 2023 Slot 3 QA Question 9

Keep going

Related Time & Work questions