Simple Interest and Compound Interest Question 3 - CAT 2022

Let the amount invested in the first part be P₁ and the second part be P₂.

The simple interest formula is SI = P × R × T / 100.

We are given that the interest earned from both parts is equal:

(P₁ × 15 × 4) / 100 = (P₂ × 12 × 3 )/ 100

60 × P₁ = 36 × P₂

Simplify the relationship by dividing both coefficients by 12:

5 × P₁ = 3 × P₂ ⇒ P₁ / P₂ = 3 / 5

This ratio implies that out of a total pool of 3 + 5 = 8 units of savings, 3 units are allocated to the first part.

Percentage in the first part = 3 / 8 × 100% = 37.5%

Correct Option: A

💡 FundaMakers Tip:

Memorize this inverse relationship for interest problems: when the interest generated from two parts is equal, the ratio of the principal investments is always inversely proportional to the product of their respective rates and timelines:

P₁ / P₂ = (R₂ × T₂) / (R₁ × T₁)

Multiplying 12 × 3 = 36 and 15 × 4 = 60 gives you an immediate inverse ratio of 36 : 60, which reduces to 3 : 5. Recognizing standard fraction values like 3 / 8 = 37.5% lets you secure the answer instantly.