A certain sum of money at simple interest amounts to Rs. 1,512 in 3 years and to Rs. 1,668 in 4.5 years. The rate of interest on this sum of money is:

Correct option is A

Given:

Amount in 3 years= ₹1512

Amount in 4.5 years = ₹1668

Formula Used:

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

Solution:

SI for 1.5 years = SI for 4.5 years - SI for 3 years

= 1668 - 1512 = ₹156

SI for one year $$= \frac{156}{1.5} =₹104$$​​

SI for 3 years =$$\frac{104}{3} =₹312$$​​

Principle = Amount - Interest = 1512 - 312 = ₹1200

​$$312 = \frac{ 1200 \times R \times 3}{100}$$​

​$$R = \frac{312 \times 100}{1200\times 3}$$​​

R = $$\frac{104}{12} =\frac{26}{3}\%$$​​