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If at same rate of interest, in 2 years

If at same rate of interest, in 2 years, the simple interest is ₹42 and compound interest is ₹51, then what is the principal (in ₹)?
यदि समान ब्याज दर पर, 2 वर्ष में साधारण ब्याज ₹ 42 तथा चक्रवृद्धि ब्याज ₹51 है, तो मूलधन (₹ में) ज्ञात कीजिए।

44 49 42 53

Detailed Solution & Logic

Correct Answer:

For 2 years,
Difference between CI and SI = 51 - 42 = 9
Also,
SI = $ \frac{P \times r \times 2}{100} = 42 $
So,
$ P r = 2100 $
For 2 years,
CI - SI = $ \frac{P r^2}{100^2} = 9 $
Substitute Pr = 2100
$ \frac{2100 \times r}{10000} = 9 $
r = $\frac{90000}{2100} $
r = $ \frac{300}{7} $
Now,
P = $ \frac{2100}{r} = \frac{2100 \times 7}{300} = 49 $
Answer = 49