The difference of simple interest from two banks on ₹8,000 in 3 years is ₹800. If the rate of interest per annum in two banks are $R_1$ and $R_2$, then what is the value of $R_1 - R_2$? (Where $R_1 R_2$)

Question

The difference of simple interest from two banks on ₹8,000 in 3 years is ₹800. If the rate of interest per annum in two banks are $R_1$ and $R_2$, then what is the value of $R_1 - R_2$? (Where $R_1 > R_2$)

Accepted Answer

**Solution:**

1. Let the principal amount be $P = 8000$.
2. The time period is $t = 3$ years.
3. The rates of interest per annum are $R_1$ and $R_2$.
4. The difference in simple interest from two banks is given as:
   $$SI_1 - SI_2 = 800$$

5. Using the simple interest formula $SI = \frac{P 	imes R 	imes t}{100}$, we write:
   $$\frac{8000 	imes R_1 	imes 3}{100} - \frac{8000 	imes R_2 	imes 3}{100} = 800$$

6. Factor out common terms:
   $$\frac{8000 	imes 3}{100} (R_1 - R_2) = 800$$

7. Calculate the constant term:
   $$\frac{24000}{100} (R_1 - R_2) = 800$$
   $$240 (R_1 - R_2) = 800$$

8. Solve for $R_1 - R_2$:
   $$R_1 - R_2 = \frac{800}{240} = \frac{10}{3} = 3 \frac{1}{3} \%$$

**Answer:** $3 \frac{1}{3} \%$

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