Given:
Interest rate= 10% per annum
Time=3 years
Simple interest (SI) = PTR/100
Where P is principle amount, T is time taken, R is rate per annum
Let sum is P
SI = (P × 3× 10)/ 100
⇒ SI = (30P)/ 100
⇒ SI = (3P)/ 10 —————- equation 1
To find the amount we have the formula,
Amount (A) = P (1+(R/100))n
Where P is present value, r is rate of interest, n is time in years.
Now substituting the values in above formula we get,
∴ CI= P (1 + 10/100)3-P
⇒ CI = P (1+1/10)3-P
⇒ CI = P (11/10)3-P
⇒ CI = P (1331) / (1000) – P
⇒ CI = 331P/1000——– equation 2
Now the difference is
(CI – SI) = 331P/1000 – (3P)/ 10
⇒ 93 = 331P- 300P/1000
⇒ 93 = 31P/1000
⇒ P= 93 × 1000/31
⇒ P= 3 × 1000
⇒ P= 3000
∴ Sum = ₹3000