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.

  1. A.

    15%

  2. B.

    12%

  3. C.

    10%

  4. D.

    14%

Attempted by 34 students.

Show answer & explanation

Correct answer: A

Key idea: use simple interest and form equations for the given amounts.

  1. Let P be the principal and r be the annual rate (in %).

  2. Write the amount equations: P(1 + 2r/100) = 1300 and P(1 + 3.5r/100) = 1525.

  3. 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.

  4. From this, Pr = 225 * 100 / 1.5 = 15000.

  5. Substitute Pr = 15000 into the first amount equation: P + 2(Pr)/100 = 1300 ⇒ P + 2(15000)/100 = 1300 ⇒ P + 300 = 1300 ⇒ P = 1000.

  6. 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.

Explore the full course: Deloitte Nla