IPMAT Indore 2026 · Quantitative Ability · Question 4

Step 1 — set up with one multiplier. Let the initial counts be 5k foreign and 8k domestic, and let f foreign workers leave alongside the 12 domestic ones.

Step 2 — the first change.

\frac{5k-f}{8k-12}=\frac{2}{3}\Rightarrow 15k-3f=16k-24 \Rightarrow 3f=24-k

Step 3 — the second change. “Replaced” means 10 leave the foreign side and 10 join the domestic side:

\frac{5k-f-10}{8k-12+10}=\frac{3}{7}\Rightarrow 7\left( 5k-f-10 \right)=3\left( 8k-2 \right)

35k-7f-70=24k-6 \Rightarrow 11k-7f=64

Step 4 — substitute. From Step 2, f=\frac{24-k}{3}:

11k-\frac{7\left( 24-k \right)}{3}=64 \Rightarrow 33k-168+7k=192 \Rightarrow 40k=360 \Rightarrow k=9

Step 5 — answer the question asked.

\text{Initial domestic}=8k=72

Check: start 45:72. Then f=5 leave with 12 domestic \to 40:60=2:3 ✓. Then 30:70=3:7 ✓

Answer: 72

Shortcut. Two traps. First, “replaced” changes both sides — -10 foreign and +10 domestic. Second, the question wants the initial domestic count 8k, not k and not the foreign count. Write down what you are solving for before you start.