A sum of Tk. 1000 was lent to two people, one at the rate of 5% and the other at the rate of 8%. If the simple interest after one year is Tk. 62, find the sum lent at 5% rate.

Question: A sum of Tk. 1000 was lent to two people, one at the rate of 5% and the other at the rate of 8%. If the simple interest after one year is Tk. 62, find the sum lent at 5% rate.

Solution:
Let the sum lent at 5% be P.
∴ Sum lent at 8 % = 1000 - P

Now, according to the question,
SI for 5% + SI for 8% = 62
⇒ (P × 5 × 1/100) + ((1000 - P) × 8 × 1/100) = 62
⇒ 5P + 8(1000 - P) = 6200
⇒ 5P + 8000 - 8P = 6200
⇒ 3P = 1800
⇒ P = 600
Therefore, sum lent at 5 % = P = Tk. 600