​If at same rate of interest, in 2 years, the simple interest is ₹60 and compound interest is ₹66, then what is the principal (in ₹)?

Correct option is B

Given:

Interest in simple interest for 2 years = ₹60

Interest in compound interest for 2 years = ₹66

Time =1.5 years

Formula Used:

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

Compounded Amount =$$Principle \times \left(1+ \frac{r}{100}\right)^{t}$$ 

CI - SI = $$P\left(\frac{R}{100}\right)^2$$​​​

Compound Interest = Amount - Principle

Solution:

Interest in simple interest is same every year hence simple interest for one year = $$\frac{60}{2}$$ = ₹30

Now the compound interest more is only the interest on the interest in first year

Hence, 66-60 = ₹6 is the interest on ₹30

Percent of 6 of 30 = $$\frac{6}{30} \times 100$$ = 20%

Let the principle sum be x

Then 20% of x = 30

x=$$\frac{100}{20} \times 30$$ = ₹150 

Alternate Solution:

Using the direct formula:

​$$6 = P\left(\frac{R}{100}\right)^2 \\ \ \\60000 = PR^2 \\ \ \\Substitute\ ( R = \frac{P}{3000} ): \\ \ \\60000 = P \left(\frac{P}{3000}\right)^2 \\ \ \\60000 = P \cdot \frac{P^2}{9,000,000} \\ \ \\60000 = \frac{P^3}{9,000,000}\\ \ \\P^3 = 60000 \times 9,000,000\\ \ \\P = \frac{60,000}{9,000,000} = ₹150$$​​