annum for $4$ years. Find the markm a bank at the rate of $8 \%$ $\newline$ markup of the bank. $\newline$ for $3$ yeem receives a profit of Rs $27$ , $000$ at the rate of $12 \%$ per $\newline$ $4$ .

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Q. annum for

4

years. Find the markm a bank at the rate of

8 \%

\newline

markup of the bank.

\newline

for

3

yeem receives a profit of Rs

27

000

at the rate of

12 \%

per

\newline

4

Calculate Total Interest Earned: First, let's calculate the total amount earned from the $8\%$ annual rate over $4$ years. We'll use the formula for simple interest: $I = P \times r \times t$ , where $I$ is the interest, $P$ is the principal amount, $r$ is the rate of interest per year, and $t$ is the time in years.
Calculate Interest at $8$ % Rate: For the $8$ % rate, let's assume the principal amount is $P$ (we'll find this value later). The rate $r$ is $8\%$ or $0.08$ , and the time $t$ is $4$ years. $\newline$ So, $I = P \times 0.08 \times 4$ .
Calculate Profit at $12\%$ Rate: Calculating the interest for the $8\%$ rate gives us $I = P \times 0.08 \times 4 = 0.32P$ .
Find Principal Amount: Now, let's calculate the profit from the $12\%$ annual rate over $3$ years. The profit is given as Rs $27,000$ , which is the interest earned at this rate. $\newline$ So, using the simple interest formula again, we have $27000 = P \times 0.12 \times 3$ .
Calculate Markup at $8$ % Rate: Solving for $P$ gives us $P = \frac{27000}{(0.12 \times 3)} = \frac{27000}{0.36} = 75000$ .
Calculate Total Amount: Now we know the principal amount $P$ is Rs $75,000$ . We can use this to find the markup for the $8\%$ rate. $\newline$ The markup is the interest at the $8\%$ rate, which we found to be $0.32P$ . $\newline$ So, the markup is $0.32 \times 75000$ .
Calculate Total Amount: Now we know the principal amount $P$ is Rs $75,000$ . We can use this to find the markup for the $8\%$ rate. $\newline$ The markup is the interest at the $8\%$ rate, which we found to be $0.32P$ . $\newline$ So, the markup is $0.32 \times 75000$ .Calculating the markup gives us $0.32 \times 75000 = 24000$ .
Calculate Total Amount: Now we know the principal amount $P$ is Rs $75,000$ . We can use this to find the markup for the $8\%$ rate. $\newline$ The markup is the interest at the $8\%$ rate, which we found to be $0.32P$ . $\newline$ So, the markup is $0.32 \times 75000$ .Calculating the markup gives us $0.32 \times 75000 = 24000$ .However, we made a mistake in the previous step. The correct calculation should be $0.32 \times 75000 = 24000$ , but we need to add the principal amount to find the total amount after $4$ years. $\newline$ So, the total amount is $75000 + 24000$ .