A certain sum of money amounts to Rs.1300 in 2 years and to Rs. 1525 in 3.5…
2025
A certain sum of money amounts to Rs.1300 in 2 years and to Rs. 1525 in 3.5 years. Find the sum and the rate of interest.
- A.
15%
- B.
12%
- C.
10%
- D.
14%
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Correct answer: A
Key idea: use simple interest and form equations for the given amounts.
Let P be the principal and r be the annual rate (in %).
Write the amount equations: P(1 + 2r/100) = 1300 and P(1 + 3.5r/100) = 1525.
Subtract the first equation from the second to eliminate P: P[(3.5r/100) - (2r/100)] = 1525 - 1300 = 225, so P*(1.5r/100) = 225.
From this, Pr = 225 * 100 / 1.5 = 15000.
Substitute Pr = 15000 into the first amount equation: P + 2(Pr)/100 = 1300 ⇒ P + 2(15000)/100 = 1300 ⇒ P + 300 = 1300 ⇒ P = 1000.
Now find r: r = Pr / P = 15000 / 1000 = 15.
Answer: The principal (sum) is Rs.1000 and the rate of interest is 15% per annum.