Jay lent some amount of money at 14% simple interest and an equal amount of money at 20% simple interest each for two years. If his total interest was, ₹9520, then find the amount of money that was lent in each case.

Correct option is D

Given:

Jay lent an equal amount of money at 14% simple interest and 20% simple interest for 2 years.

Total interest earned = ₹9,520.

Concept Used:

The formula for simple interest is:

Simple Interest = $$\frac{P \times R \times T}{100}$$​​

where:

P is the principal,

R is the rate of interest,

T is the time in years.

Let the amount of money lent in each case be x.

Solution:

Interest from the loan at 14% for 2 years:

Interest = $$\frac{x \times 14 \times 2}{100} = \frac{28x}{100} = 0.28x$$​​

Interest from the loan at 20% for 2 years:

Interest = $$\frac{x \times 20 \times 2}{100} = \frac{40x}{100} = 0.40x$$​​

The total interest from both loans is the sum of the individual interests:

0.28x + 0.40x = 9,520

0.68x = 9,520

x = $$\frac{9,520}{0.68}$$​ = 14,000

The amount of money lent in each case is ₹14,000.

Thus, the correct option is (d)  ₹14,000

Alternate Method:

Let invested Rs x,

​$$\frac{P\times 14 \times 2}{100} + \frac{P \times 20 \times 2}{100} = 9520$$

=> 68 P = 952000

=> P = 14000​​