IPMAT Indore 2025 · Quantitative Ability · Question 8

Step 1 — name the unknown. Let Nikita alone need n days for the whole job. Then in one day Nikita does \frac{1}{n} of the job.

Step 2 — use the “together” information. Together they finish in 12 days, so their one-day work adds up to \frac{1}{12}:

\text{Arpita’s one-day work}=\frac{1}{12}-\frac{1}{n}=\frac{n-12}{12n}

Step 3 — write the time for each stretch. Arpita alone does 40% of the job, so the time she takes is \frac{0.4}{\text{her one-day work}}, and Nikita alone does the other 60%:

\underset{\text{Arpita’s time}}{\underset{⏟}{\frac{0.4\times 12n}{n-12}}}+ \underset{\text{Nikita’s time}}{\underset{⏟}{0.6\,n}}= 24

Step 4 — solve. Multiply through by \left( n-12 \right):

4.8n+0.6n\left( n-12 \right)=24\left( n-12 \right)

0.6{n}^{2}-26.4n+288=0 \Rightarrow{n}^{2}-44n+480=0

\left( n-20 \right)\left( n-24 \right)=0 \Rightarrow n=20\text{or}n=24

Step 5 — check both. Both genuinely work, which is why the question says possible:

n=20: Arpita needs 30 days alone, so 40% takes her 0.4\times 30=12 days; Nikita’s 60% takes 0.6\times 20=12 days. Total =24. ✓

n=24: Arpita also needs 24 days alone, so 40% takes 9.6 days and Nikita’s 60% takes 14.4 days. Total =24. ✓

Answer: 20 (24 is equally defensible and is accepted here as an alternative).