Question

Q.9 Find Rate and Time when : (i) P = 500, T = 146 Days and S.l. = 164 (ii) P = 1600, R = 10% and S.l. = 400​

Answer 1

➤ First Answer:

➣ Given:-

• Principal = Rs. 500
• Time = 146 days = 2/5 years = 0.4 years
• Simple Interest = Rs. 164

➣ What To Find:-

We have to find the

• Rate

➣ Formula For Finding:-

The Formula:

$\bf Rate = \dfrac{100 \times Simple \: Interest}{Principal \times Time}$

➣ Solution:-

Using the formula,

$\sf \Longrightarrow Rate = \dfrac{100 \times Simple \: Interest}{Principal \times Time}$

Substitute the values,

$\sf \Longrightarrow Rate = \dfrac{100 \times 164 \times 2}{500 \times 5}$

Cancel the zeros,

$\sf \Longrightarrow Rate = \dfrac{1 \!\!\!\not 0 \!\!\!\not0 \times 164 \times 2}{5\!\!\!\not 0 \!\!\!\not0 \times 5}$

Also written as,

$\sf \Longrightarrow Rate = \dfrac{164 \times 2}{5 \times 5}$

Multiply the numerator,

$\sf \Longrightarrow Rate = \dfrac{328}{5 \times 5}$

Multiply the denominator,

$\sf \Longrightarrow Rate = \dfrac{328}{25}$

Divide 328 by 25,

$\sf \Longrightarrow Rate = 13.12 \: \%$

∴ Therefore, the rate is 13.12 %.

—————————————————————

➤ Second Answer:

➣ Given:-

• Principal = Rs. 1600
• Rate = 10 %
• Simple Interest = Rs. 400

➣ What To Find:-

We have to find the

• Time

➣ Formula For Finding:-

The Formula:

$\bf Time = \dfrac{100 \times Simple \: Interest}{Principal \times Rate}$

➣ Solution:-

Using the formula,

$\sf \Longrightarrow Time = \dfrac{100 \times Simple \: Interest}{Principal \times Rate}$

Substitute the values,

$\sf \Longrightarrow Time = \dfrac{100 \times 400}{1600 \times 10}$

Cancel the zeros,

$\sf \Longrightarrow Time = \dfrac{1 \!\!\!\not 0 \!\!\!\not 0 \times 40 \!\!\!\not 0}{16 \!\!\!\not 0 \!\!\!\not 0 \times 1 \!\!\!\not 0}$

Also written as,

$\sf \Longrightarrow Time = \dfrac{40}{16}$

Divide 40 by 16,

$\sf \Longrightarrow Time = 2.5 \: years$

∴ Therefore, the time is 2.5 years.

—————————————————————