IPMAT Indore 2026 · Quantitative Ability · Question 18

IPMAT Indore 2026 previous year question on Time and Work, with the answer and a step-by-step solution.

Time and WorkArithmeticMultiple choiceMedium

Painter A can paint a building in 12 days while Painter B can paint it in 16 days. If A and B work on alternate days, and A starts the work on the first day, then the number of days required to paint the building is

A
7\frac{6}{7}
B
13\frac{2}{3}
C
13\frac{3}{4}
D
13\frac{1}{2}

Pick an option, then check.

Answer & solution

Answer: Option B

Step 1 — put the work on a common scale. Take the building as \text{lcm}\left( 12,16 \right)=48 units.

\text{A’s rate}=\frac{48}{12}=4\text{units/day}, \text{B’s rate}=\frac{48}{16}=3\text{units/day}

Step 2 — look at a two-day block. A works day 1, B day 2:

4+3=7\text{units every 2 days}

Step 3 — run as many full blocks as possible.

6\text{blocks}=12\text{days}=42\text{units}

Remaining: 48-42=6 units.

Step 4 — finish off day by day. Day 13 is A’s turn: she adds 4 units, total 46. Remaining 2 units.

Day 14 is B’s turn, at 3 units/day:

\text{time needed}=\frac{2}{3}\text{of a day}

Step 5 — total.

13+\frac{2}{3}=13\frac{2}{3}\text{days}

Answer: Option 2 — 13\frac{2}{3}

Shortcut. Never divide 48 by the two-day average — alternate-day problems must be run in blocks and then finished one day at a time, because the last worker may not need a full day. The fractional part always comes from the final partial day.

IPMAT Indore 2026 · Quantitative Ability · Question 18

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