A and B can do a work in 9 days and 12… - CUET UG 2023 General Test PYQ

CUET UG 2023 — General Test Arithmetic

2023mcqmedium

A and B can do a work in 9 days and 12 days respectively. If they work on alternate days starting with A, then in how many days will the work be completed?

Official previous-year question

Held on 21 May 2023 · Verified 13 Jul 2026.

Options

A
36 days
B
10 days
C
$10\frac{1}{4}$ days
D
13 days

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Solution

A's 1-day work = $\frac{1}{9}$ , B's 1-day work = $\frac{1}{12}$ .

In 2 days (A then B): $\frac{1}{9} + \frac{1}{12} = \frac{7}{36}$ .

In 10 days (5 cycles): $\frac{35}{36}$ work done. Remaining: $\frac{1}{36}$ .

On day 11, A works: time = $\frac{1/36}{1/9} = \frac{1}{4}$ day.

Total = $10\frac{1}{4}$ days.

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