CUET CUET Mathematics 2024 - Ms. Sheela creates a fund of ₹ 1,00,000 for providing scholarships to needy children. The scholarship is provided in the beginning of the year. This fund earns an interest of r \% per annum. If the scholarship amount is taken as ₹ 8,000, then r= | PYQs + Solutions

CUET Mathematics 2024

Statistics & Applications

Financial Math

Medium

Ms. Sheela creates a fund of ₹ $1,00,000$ for providing scholarships to needy children. The scholarship is provided in the beginning of the year. This fund earns an interest of $r \%$ per annum. If the scholarship amount is taken as ₹ $8,000$ , then $r=$

8 \frac{1}{2} \%

8 \frac{16}{23} \%

8 \frac{17}{25} \%

8 \frac{2}{5} \%

Correct Option: 2

I'll solve this with cleaner, multi-line equations.

Given:

\newline

- Initial fund:

₹1,00,000

\newline

- Scholarship amount:

₹8,000

(given at beginning of year)

\newline

- Interest rate:

r\%

per annum

Since the scholarship is given at the beginning of the year, the remaining amount is:

\newline

₹1,00,000 - ₹8,000 = ₹92,000

This amount must grow to

₹1,00,000

by year-end:

\newline

₹92,000 \times (1 + \frac{r}{100}) = ₹1,00,000

Solving for

r

\newline

1 + \frac{r}{100} = \frac{1,00,000}{92,000}

\frac{r}{100} = \frac{1,00,000}{92,000} - 1

\frac{r}{100} = \frac{1,00,000 - 92,000}{92,000}

\frac{r}{100} = \frac{8,000}{92,000}

r = 100 \times \frac{8,000}{92,000}

r = 100 \times \frac{8}{92}

r = 100 \times \frac{2}{23}

r = \frac{200}{23} = 8\frac{16}{23}\%

Therefore,

r = 8\frac{16}{23}\%

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CUET Mathematics 2024

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