A sum of Rs 8000 is divided into two parts. The simple interest on the first part at the rate of 21% per annum for one year is equal to the simple interest on the second part at the rate of 35% per annum for the same one year. Using this condition about equal interest on both parts, what is the simple interest, in rupees, earned on each part in that year?

Introduction / Context:
This question involves dividing a total sum into two parts such that the simple interests on the two parts, at different rates, are equal over the same time period. These types of problems test a candidate’s skill in translating a verbal condition about equal interests into an equation involving the two parts of the principal. Once the relation is established, the problem reduces to solving a simple linear equation and then computing the interest on either part using the standard simple interest formula.

Given Data / Assumptions:

• Total sum of money = Rs 8000.
• First part is invested at 21% per annum simple interest for 1 year.
• Second part is invested at 35% per annum simple interest for 1 year.
• Simple interest on the first part equals simple interest on the second part.
• Time period is one year for both parts.

Concept / Approach:
For simple interest, we use:
SI = (P * R * T) / 100 Let the first part be x rupees, then the second part is 8000 − x rupees. The interests on both parts for one year can be computed in terms of x. The condition that these interests are equal gives an equation that can be solved for x. After finding x, we can compute the simple interest on either part, which will be the same value and is what the question asks for.

Step-by-Step Solution:
Let the first part be x rupees. Then the second part is 8000 − x rupees. Interest on the first part for 1 year at 21%: SI1 = (x * 21 * 1) / 100 = 0.21x. Interest on the second part for 1 year at 35%: SI2 = ((8000 − x) * 35 * 1) / 100 = 0.35 * (8000 − x). Given SI1 = SI2, so 0.21x = 0.35 * (8000 − x). 0.21x = 0.35 * 8000 − 0.35x = 2800 − 0.35x. Bring like terms together: 0.21x + 0.35x = 2800. 0.56x = 2800. x = 2800 / 0.56 = 5000. So the first part is Rs 5000 and the second part is 8000 − 5000 = Rs 3000. Simple interest on the first part: SI1 = 0.21 * 5000 = Rs 1050. Simple interest on the second part: SI2 = 0.35 * 3000 = Rs 1050. Therefore, the interest earned on each part is Rs 1050.

Verification / Alternative check:
We can verify the arithmetic quickly. For Rs 5000 at 21% for 1 year, 21% of 5000 is 0.21 * 5000 = 1050. For Rs 3000 at 35% for 1 year, 35% of 3000 is 0.35 * 3000 = 1050. Since both interests are equal and match the condition, and the total of the two parts is still Rs 8000, our solution is consistent and correct.

Why Other Options Are Wrong:
Rs 840, Rs 1400, Rs 1220, and Rs 700 do not match the equal interest condition when we check with correct principal values. If the interest were Rs 840, the parts would not sum to Rs 8000 under the given rates. Similar inconsistencies arise for the other incorrect options. Only Rs 1050 satisfies both the simple interest formula for each part and the equality condition.

Common Pitfalls:
One common mistake is to assume the two parts are equal (each Rs 4000), which does not satisfy the equal interest condition at different rates. Another error is misapplying the simple interest formula without dividing by 100 or mishandling decimals. Some learners also incorrectly treat the rates as if they apply to the same principal. Writing the equation systematically and double checking each algebraic step prevents such errors.

Final Answer:
The simple interest earned on each part of the investment for that year is Rs 1050.