If at the same rate of interest, in 2 years, the simple interest is Rs. 42 and the compound interest is Rs. 49, then what is the principal?

Correct option is D

Given:
SI = 42
CI = 49
Time = 2 years
Formula Used:
​$$\text{CI} - \text{SI} = P \left(\frac{R}{100}\right)^2$$​​
Solution:
49 − 42 = 7
​$$7 = P \times \left(\frac{R}{100}\right)^2 \quad (1)\\\ \\\text{Also,}\\\ \\\text{SI} = \frac{P \times R \times 2}{100}\\\ \\42 = \frac{2PR}{100}\\\ \\PR = 2100 \quad (2)\\\ \\\text{From (2):}\\\ \\R = \frac{2100}{P}\\\ \\\text{Substitute in (1):}\\\ \\7 = P \times \left(\frac{2100}{100P}\right)^2\\\ \\P = 63$$​​