Question

Nidhi received simple interest of ₹1,200 when she invested ₹x at 6% per annum and ₹y at 5% per annum for 1 year. Had she invested ₹x at 3% per annum and ₹y at 8% per annum for that year, she would have received simple interest of ₹1,260.Find the values of x and y.

Answer 1

Simple Interest Problem

Formula: \[ \text{Simple Interest (SI)} = \frac{P \times R \times T}{100} \] where:

• \( P \): Principal
• \( R \): Rate of interest
• \( T = 1 \): Time in years

Case 1

• Amount \( x \) invested at 6% p.a.:
• Amount \( y \) invested at 5% p.a.:
• Total Interest = ₹1200:

Case 2

• Amount \( x \) invested at 3% p.a.:
• Amount \( y \) invested at 8% p.a.:
• Total Interest = ₹1260:

Solving the System of Equations

Multiply Equation (2) by 2 to align coefficients of \( x \):

\[ 6x + 16y = 252000 \quad \text{(Equation 3)} \]

Subtract Equation (1) from Equation (3):

\[ (6x + 16y) - (6x + 5y) = 252000 - 120000 \Rightarrow 11y = 132000 \Rightarrow y = \frac{132000}{11} = 12000 \]

Substitute \( y = 12000 \) into Equation (1):

\[ 6x + 5(12000) = 120000 \Rightarrow 6x + 60000 = 120000 \Rightarrow 6x = 60000 \Rightarrow x = \frac{60000}{6} = 10000 \]

✅ Final Answer:

\[ x = \boxed{₹10{,}000}, \quad y = \boxed{₹12{,}000} \]