A man invests ₹ 1550 in two parts, one part at the rate of 8 % interest and…

Concept: For a one-year deposit, simple interest is I = P × R / 100, where P is the principal and R is the annual rate in percent. When a single sum is split into two parts placed at different rates, two conditions hold together: the two parts add back to the original sum, and the total interest is the sum of the interest earned by each part separately. Naming one part x turns those two conditions into a single linear equation in one unknown.

Application:

1. Let ₹x be the part invested at 8% per annum.

2. The remaining part, invested at 6% per annum, is then ₹(1550 − x).

3. Interest from the first part in one year = x × 8/100 = 0.08x.

4. Interest from the second part in one year = (1550 − x) × 6/100 = 93 − 0.06x.

5. The total interest for the year is ₹106, so 0.08x + 93 − 0.06x = 106.

6. Combining like terms gives 0.02x = 13, hence x = 13 ÷ 0.02 = 650.

7. Substituting back, the remaining part is ₹1550 − ₹650 = ₹900.

Cross-check: ₹650 at 8% earns 650 × 8/100 = ₹52 and ₹900 at 6% earns 900 × 6/100 = ₹54; these add to ₹106, and the parts themselves add to ₹1550, so both given conditions are satisfied. Working out every offered split makes the difference explicit:

Because the amounts are asked in the order in which the rates are quoted — the 8% part first and the 6% part second — the required amounts are ₹650 and ₹900.