Shortcut Trick
Ratio of shares when amounts are equal at CI = (1 + R/100)Time Diff.
Time difference = 15 − 14 = 1 year.
Ajay's Share : Prakash's Share = (1 + 10/100)1 = 11 : 10.
Prakash's share = (10 / 21) × 1218 = 10 × 58 = ₹580.
∴ The correct answer is ₹580.
Alternate Method
Given:
Total amount = ₹1218
Time for Ajay (T1) = 14 years
Time for Prakash (T2) = 15 years
Rate of Interest (R) = 10%
Formula Used:
A = P(1 + R/100)n
Total = ₹1218
Ajay (Share: A)
T = 14 yrs, R = 10%
Prakash (Share: P)
T = 15 yrs, R = 10%
Amounts are Equal → A / P = 11 / 10
Calculations:
⇒ Let Ajay's share be A and Prakash's share be P.
⇒ Amount of Ajay after 14 years = A × (1 + 10/100)14
⇒ Amount of Prakash after 15 years = P × (1 + 10/100)15
⇒ Since both amounts are equal:
⇒ A × (11/10)14 = P × (11/10)15
⇒ A / P = (11/10)15 − 14
⇒ A / P = 11 / 10
⇒ The ratio of shares of Ajay and Prakash is 11 : 10
⇒ Total ratio parts = 11 + 10 = 21 parts
⇒ Value of 21 parts = ₹1218
⇒ Value of 1 part = 1218 / 21 = 58
⇒ Prakash's share (10 parts) = 10 × 58 = ₹580
∴ The correct answer is ₹580.
Additional Information
Compound Interest Formula
Amount = P(1 + R/100)n, where P is the principal sum, R is the rate of interest, and n is the time period in years.
Division of Amount in CI
If a total sum is divided into two parts P1 and P2 such that their amounts after t1 and t2 years respectively at R% CI are equal, then P1 / P2 = (1 + R/100)t<sub>2</sub> − t<sub>1</sub>. The person with less time gets a larger share of the principal.
Simple Interest vs Compound Interest
In Simple Interest, the principal remains constant throughout the period. In Compound Interest, the interest earned in previous periods is added to the principal for the calculation of interest in subsequent periods.