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CAT 2025 Slot 2 QA Question 10

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

CAT 2025 Slot 2QAArithmetic • Time & WorkModerate
Ankita is twice as efficient as Bipin, while Bipin is twice as efficient as Chandan. All three of them start together on a job, and Bipin leaves the job after 20 days. If the job got completed in 60 days, the number of days needed by Chandan to complete the job alone, is
TITA Answer:
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Answer and solution

Answer: 340

📌 Core Concept
The problem involves combined work rates. The formula used is:
Work=Rate×Time\text{Work} = \text{Rate} \times \text{Time}
🔢 Step-by-Step Solution
1
Define Efficiency:
Let Chandan's efficiency be CC.
Bipin's efficiency is 2C2C.
Ankita's efficiency is 4C4C.
2
Work Done in First 20 Days:
All three work together.
Combined rate: 4C+2C+C=7C4C + 2C + C = 7C.
Work done: 7C×20=140C7C \times 20 = 140C.
3
Work Done Next 40 Days:
Only Ankita and Chandan work.
Combined rate: 4C+C=5C4C + C = 5C.
Work done: 5C×40=200C5C \times 40 = 200C.
4
Total Work Equation:
140C+200C=1140C + 200C = 1 (since total work is 1 job).
340C=1340C = 1.
C=1340C = \frac{1}{340}.
5
Chandan's Time Alone:
Time = 1C\frac{1}{C} = 340$ days.
⚡ 30-Second Shortcut
Assign variables based on efficiency ratios.
Break work into segments with different participants.
Sum the work segments and solve for the unknown variable.
🎯 Final Answer
Correct Answer: 340

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