Two equal amounts of money are lent out a 6% and 5% simple interest…
2025
Two equal amounts of money are lent out a 6% and 5% simple interest respectively at the same time . The former is recovered two years earlier than the latter and the amount so recovered in each case is Rs 2800 . Determine the amount that is lent out ?
- A.
1800
- B.
1500
- C.
1750
- D.
1375
Attempted by 4 students.
Show answer & explanation
Correct answer: C
Let the principal (each amount lent) be P.
Let the time for the loan at 6% be t years. Since this loan is recovered two years earlier than the loan at 5%, the time for the 5% loan is t + 2 years.
Both final amounts are equal to Rs 2800, so:
P(1 + 6t/100) = 2800
P(1 + 5(t + 2)/100) = 2800
Eliminate P by equating the two bracketed expressions:
1 + 6t/100 = 1 + 5(t + 2)/100
Solve for t: 6t = 5t + 10 ⇒ t = 10 years.
Substitute t = 10 into one final-amount equation to find P:
P(1 + 6·10/100) = 2800 ⇒ P × 1.6 = 2800 ⇒ P = 2800 / 1.6 = 1750
Answer: Rs 1750.