Question

A sum of ₹15400 is lent out in two parts in such a way that the interest on one part at 20% for 5 years is equal to that on another at 9% for 6 years. The sum (in ₹) lent out at 20% interest is:

• A. ₹10000
• B. ₹2700
• C. ₹5400
• D. ₹1350

Hint:

If $SI_1 = SI_2$, then the ratio of principal is $P_1 : P_2 = (R_2T_2) : (R_1T_1)$. Here: $P_1 : P_2 = (9 \times 6) : (20 \times 5) = 54 : 100$.

Answer 1

The Correct Option is C

Concept: Simple Interest (SI) $= \frac{P \times R \times T}{100}$. If interests are equal, we can set up an inverse ratio of the products of Rate and Time.

Step 1: Set up the interest equality.
Let the two parts be $P_1$ and $P_2$.
$\frac{P_1 \times 20 \times 5}{100} = \frac{P_2 \times 9 \times 6}{100}$
$100 P_1 = 54 P_2$
$\frac{P_1}{P_2} = \frac{54}{100} = \frac{27}{50}$.

Step 2: Divide the total sum.
The ratio of $P_1 : P_2 = 27 : 50$.
Total parts $= 27 + 50 = 77$.
Value of 1 part $= 15400 \div 77 = ₹200$.

Step 3: Calculate the specific part.
$P_1$ (at 20%) $= 27 \text{ parts} \times ₹200 = ₹5400$.