IPMAT Indore 2025 · Quantitative Ability · Question 12

Step 1 — set up notation. Let

x = students who did not appear for Maths, so 2x did not appear for English

{E}_{f} = appeared for English but failed

{M}_{f} = appeared for Maths but failed

For each subject, every one of the 120 students either did not appear, appeared and failed, or appeared and passed.

Step 2 — translate the two “twice” conditions.

\text{passed Maths}=2{E}_{f}, \text{passed English}=2{M}_{f}

Step 3 — write one equation per subject (they must each total 120).

Maths: x+{M}_{f}+2{E}_{f}=120 \Rightarrow 2{E}_{f}+{M}_{f}=120-x \ldots (i)

English: 2x+{E}_{f}+2{M}_{f}=120 \Rightarrow{E}_{f}+2{M}_{f}=120-2x \text{…(ii)}

Step 4 — the trick: add and subtract.

Subtracting (ii) from (i): {E}_{f}-{M}_{f}=x

Adding (i) and (ii): 3{E}_{f}+3{M}_{f}=240-3x \Rightarrow{E}_{f}+{M}_{f}=80-x

Now add those two results — the x cancels:

2{E}_{f}=80 \Rightarrow{E}_{f}=40

Notice we never needed the value of x at all.

Answer: 40