The amount obtained by Sumit by investing a sum of Rs 10,920 for 3 years at the rate of 10% simple interest is equal to the amount obtained by Raghav by investing a certain sum in Rs for 5 years at the rate of 8% per annum SI. What is 85% of the sum invested by Raghav?

First, we need to calculate the amount obtained by Sumit. The formula for simple interest is:

Interest = Principal * Rate * Time

So, Sumit's total amount (Principal + Interest) will be:

Amount = Principal + Interest Amount = Rs 10,920 + (10,920 * 10/100 * 3) Amount = Rs 10,920 + Rs 3,276 Amount = Rs 14,196

This is the same amount that Raghav gets. The formula for simple interest can be rearranged to find the principal:

Principal = Interest / (Rate * Time)

So, the sum invested by Raghav is:

Sum = Amount / (1 + Rate * Time) Sum = Rs 14,196 / (1 + 8/100 * 5) Sum = Rs 14,196 / 1.4 Sum = Rs 10,140

Finally, we need to find 85% of this sum:

85% of Sum = 85/100 * Rs 10,140 85% of Sum = Rs 8,619

So, 85% of the sum invested by Raghav is Rs 8,619.