IPMAT Indore 2024 · Quantitative Ability · Question 36

Step 1 — convert scheme A to its half-yearly terms. 10\% per annum compounded half-yearly means 5\% per half-year for 2 periods. If Rs. x goes into A, its value after one year is

x{\left( 1.05 \right)}^{2}=1.1025\,x

Step 2 — scheme B. The remaining Rs. \left( 10000-x \right) at 12\% simple interest for one year is worth

\left( 10000-x \right)\left( 1.12 \right)

Step 3 — use the given gap.

\left( 10000-x \right)\left( 1.12 \right)-1.1025x=2310

11200-1.12x-1.1025x=2310

2.2225x=8890 \Rightarrow x=4000

So Rs. 4000 in A and Rs. 6000 in B.

Step 4 — compute each interest.

A: 4000\times 0.1025=410, B: 6000\times 0.12=720

\text{Total}=410+720=1130

Check: values are 4410 and 6720; difference =2310 ✔

Answer: Option 2 — 1130

Shortcut. Memorise the effective rate. 10\% compounded half-yearly is exactly 10.25\% effective for one year — that single number replaces the whole {\left( 1.05 \right)}^{2} computation.

Then the split follows from a clean subtraction:

1.12\left( 10000-x \right)-1.1025x=2310 \Rightarrow x=4000

and the total interest is 410+720=1130.

Estimate first if time is short: the whole 10000 at 12% would give 1200, and shifting part of it to a 10.25% scheme pulls the total a little below that. Only option (b) sits just under 1200 in a plausible way.