A sum was lent out for a certain time. The sum amounts to ₹ 400 at 10% annual interest rate. When the sum was lent out at 4% annual interest rate,it amounts to ₹ 200. Find the sum.

According to the question,
[P + (P x R x T)/100] - [P + (P x 4 x T)/100] = 400 - 200
⇒ (6 x PT) / 100 = 200
⇒ PT = (200 x 100)/6 = 10000/3
Again, for 10% rate,
SI= (P x 10 x T)/100 = (10000/3) x (10/100) = 1000/3
∴ Sum(P) = 400 - (1000/3) = (1200 - 1000/3
= ₹ 200/3