IPMAT Indore 2023 · Quantitative Ability · Question 3

IPMAT Indore 2023 previous year question on Time and Work, with the answer and a step-by-step solution.

Time and WorkArithmeticType in the answer (TITA)Medium

Amisha can complete a particular task in twenty days. After working for four days she fell sick for four days and resumed the work on the ninth day but with half of her original work rate. She completed the task in another twelve days with the help of a co-worker who joined her from the ninth day. The number of days required for the co-worker to complete the task alone would be _____

Answer & solution

Answer: 24

Step 1 — Amisha’s rates. Her full rate is \frac{1}{20} of the task per day; her halved rate is \frac{1}{40}.

Step 2 — account for the work in three phases.

Phase	Days	Who works	Work done
Days 1–4	4	Amisha at full rate	4\times 1/20=1/5
Days 5–8	4	nobody (she is ill)	0
Days 9–20	12	Amisha at half rate + co-worker	12\times 1/40+12r

Step 3 — set the total to one whole task. Let the co-worker’s rate be r per day.

\frac{1}{5}+\frac{12}{40}+12r=1

\frac{4}{20}+\frac{6}{20}+12r=1 \Rightarrow \frac{10}{20}+12r=1 \Rightarrow 12r=\frac{1}{2}

Step 4 — invert.

r=\frac{1}{24}\Rightarrow \text{the co-worker alone needs}24\text{days}

Answer: 24

Shortcut. Work in units, not fractions. Let the task be 40 units (the lcm of 20 and 40). Amisha does 2 units/day at full rate, 1 unit/day at half rate.

Days 1–4: 4\times 2=8 units

Days 9–20: 12\times 1=12 units

That is 20 of the 40 units, so the co-worker supplies the other 20 units in 12 days. Alone, he needs

\frac{40}{20/12}=24\text{days}

The sick days are a red herring — they contribute nothing and only exist to make you lose track of the day count. Tabulating the phases prevents that.

IPMAT Indore 2023 · Quantitative Ability · Question 3

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