Answer:
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Explanation:
Let's start by calculating the interest received by Ram and Shyam.
Ram invested Rs. 50,000 for 3 years at 12% simple interest per annum. The formula to calculate simple interest is:
Simple Interest = (P * R * T) / 100
where P is the principal amount (in this case, Rs. 50,000), R is the rate of interest (12%), and T is the time period (3 years).
So, the simple interest received by Ram is:
Simple Interest = (50,000 * 12 * 3) / 100 = Rs. 18,000
Shyam invested the same amount (Rs. 50,000) for the same time (3 years) at the rate of 10% annual compound interest. The formula to calculate compound interest is:
Compound Interest = P * (1 + R/100)^T - P
where P is the principal amount (in this case, Rs. 50,000), R is the rate of interest (10%), and T is the time period (3 years).
So, the compound interest received by Shyam is:
Compound Interest = 50,000 * (1 + 10/100)^3 - 50,000 = Rs. 16,105.
Therefore, the interest received by Ram is Rs. 18,000 and the interest received by Shyam is Rs. 16,105.
To calculate how much more or less amount Ram should invest for equal interest, we can use the following formula:
(P1 * R * T) / 100 = P2 * (1 + R/100)^T - P2
where P1 is the amount invested by Ram, P2 is the amount invested by Shyam, R is the rate of interest (12%), and T is the time period (3 years).
We can rearrange this formula to solve for P1:
P1 = [P2 * (1 + R/100)^T - P2] * 100 / (R * T)
Substituting the values, we get:
P1 = [50,000 * (1 + 10/100)^3 - 50,000] * 100 / (12 * 3) ≈ Rs. 39,780
So, if Ram had invested Rs. 39,780 instead of Rs. 50,000 for 3 years at 12% simple interest per annum, he would have received the same interest as Shyam.