IPMAT Indore 2024 · Quantitative Ability · Question 10

Step 1 — name the unknown. Let Rs. x be lent at 3\%; then Rs. \left( 4000-x \right) is at 4\%. Both run for 4 years.

Step 2 — write the simple interest. Using SI=\frac{P\times R\times T}{100}:

\frac{x\times 3\times 4}{100}+\frac{\left( 4000-x \right)\times 4\times 4}{100}=520

Step 3 — simplify.

12x+16\left( 4000-x \right)=52000

12x+64000-16x=52000 \Rightarrow -4x=-12000 \Rightarrow x=3000

Check. 3000 at 3\% for 4 years =360; 1000 at 4\% for 4 years =160; total =520 ✔

Answer: Rs. 3000

Shortcut. Alligation on the rate. Over 4 years the total interest is Rs. 520 on Rs. 4000, an effective rate of

\frac{520}{4000\times 4}=3.25\% \text{per annum.}

Now alligate 3\% and 4\% about 3.25\%: the distances are 0.75 and 0.25, so the amounts are in the ratio 0.75:0.25=3:1 in favour of the 3% part. Hence 3/4\times 4000=3000. Mental arithmetic, no equation.