Q16 of 52 Page 112

If simple interest of a certain sum of money for 1 year is ₹50 and compound interest for 2 years is ₹102, let us write by calculating the sum of money and the rate of interest.

Let the principal = ₹p and the rate of interest per annum = r%


∴ The interest for 1 year at the rate of simple interest r% per annum



Again the amount at the rate of compound interest r% per annum for 2 years


∴ Compound interest for 2 years




By the condition, … (1)


… (2)


Dividing equation (2) by (1),





⇒ 1/2 r = 102 – 100


⇒ 1/2 r = 2


⇒ r = 2 × 2


∴ r = 4


From (1),





⇒ p = 50 × 25


∴ p = 1250


∴ Principal is ₹1250 and rate of interest is 4%.


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