IPMAT Indore 2022 · Quantitative Ability · Question 23

Step 1 — write the combined average.

\frac{160n+172m}{n+m}=164

Step 2 — clear the denominator.

160n+172m=164n+164m

8m=4n \Rightarrow \frac{m}{n}=\frac{4}{8}=\frac{1}{2}

m:n=1:2

Check: take n=2, m=1. Total height =2\left( 160 \right)+172=492 over 3 people =164 ✔

Answer: Option 1 — 1:2

Shortcut. Alligation gives this in one line. Place the two group averages either side of the combined average:

\begin{matrix}160 & & 172 \\ & 164 & \end{matrix}

The distances are 164-160=4 and 172-164=8, and the groups are in the inverse ratio of those distances:

n:m=8:4=2:1 \Rightarrow m:n=1:2

The trap is the order. The question asks for m:n, not n:m — and 2:1 is sitting there as option (d). Read which ratio is wanted before you write the answer; alligation naturally produces the ratio of the group sizes in the order you set up the diagram.