To determine how many paise per rupee per year Rs 510 will amount to Rs 595 in 8 months using simple interest, we need to follow these steps:
1. Identify the given values:
- Principal ([tex]\(P\)[/tex]): Rs 510
- Amount ([tex]\(A\)[/tex]): Rs 595
- Time ([tex]\(T\)[/tex]): 8 months
2. Calculate the interest accrued ([tex]\(I\)[/tex]):
[tex]\[
I = A - P = 595 - 510 = 85 \text{ Rs}
\][/tex]
3. Convert the time from months to years:
[tex]\[
T = \frac{8 \text{ months}}{12 \text{ months/year}} = \frac{2}{3} \text{ years}
\][/tex]
4. Use the formula for simple interest to calculate the rate of interest ([tex]\(R\)[/tex]) in percentage per annum:
[tex]\[
I = \frac{P \times R \times T}{100}
\][/tex]
Substituting the known values:
[tex]\[
85 = \frac{510 \times R \times \frac{2}{3}}{100}
\][/tex]
Rearrange to solve for [tex]\(R\)[/tex]:
[tex]\[
85 = \frac{510 \times R \times 2}{300}
\][/tex]
[tex]\[
85 = \frac{1020R}{300}
\][/tex]
Multiply both sides by 300:
[tex]\[
85 \times 300 = 1020R
\][/tex]
[tex]\[
25500 = 1020R
\][/tex]
Divide both sides by 1020:
[tex]\[
R = \frac{25500}{1020} = 25 \% \text{ per annum}
\][/tex]
5. Convert the rate of interest from percentage per annum to paise per rupee per annum:
Since 1% per annum equals 100 paise per annum:
[tex]\[
25 \% \text{ per annum} = 25 \times 100 = 2500 \text{ paise per rupee per annum}
\][/tex]
6. Check against the given options to find the closest option for paise per rupee per year:
The closest option is:
d) 36 paise (closest to the computed rate of 2500 paise per rupee per annum).
So, the rate of interest in paise per rupee per year will be closest to the option:
d) 36 paise.
