Question

The difference between the simple interest of 7 years and 10 years of a money is 150 rupees. If the rate of interest is 5% per annum, find the money.​

Answer 1

${\bold{\underline{\underline{Answer:}}}}$

${\bold{\therefore Principal=1000\:rupees}}$

${\bold{\underline{\underline{Step-by-step\:explanation:}}}}$

• In the given question information given about the difference between the simple interest of 7 years and 10 years of a money is 150 rupees. If the rate of interest is 5% per annum.

• We have to find the money.

$\underline \bold{Given : } \\ \implies Difference = 150 \: rupees \\ \\ \implies Rate = 5\% \\ \\ \implies T_{1} = 7 \: years \\ \\ \implies T_{2} = 10 \: years \\ \\ \underline \bold{To \: Find : } \\ \implies Principal = ?$

• According to given question :

$\bold{For \: 10 \: years : } \\ \implies S.I= \frac{P \times R\times T}{100} \\ \\ \implies S.I_{1} = \frac{P \times 5 \times 10}{100} \\ \\ \bold{\implies S.I_{1} = \frac{P}{2} } \\ \\ \bold{For \: 7 \: years : } \\ \implies S.I_{2} = \frac{P \times R \times T}{100} \\ \\ \implies S.I_{2} = \frac{P \times 5 \times 7}{100} \\ \\ \bold{ \implies S.I_{2} = \frac{7P}{20}} \\ \\ \bold{for \: difference : } \\ \implies S.I_{1} - S.I_{2} = 150 \\ \\ \implies \frac{P}{2} - \frac{7P}{20} = 150 \\ \\ \implies \frac{10P - 7P}{20} = 150 \\ \\ \implies 3P = 3000 \\ \\ \bold{\implies P = 1000 \: rupees}$

Answer 2

Answer:

• P= 1000 rupees

Step-by-step explanation:

○Given:

□Rate= 5%

□Time(1)= 7 years

□Time(2)= 10 years

□Difference= 150

$\bold{For \: 10 \: years : } \\ \to S.I(1)= \frac{p \times r\times t}{100} \\ \\ \to S.I(1 )= \frac{p \times 5 \times 10}{100} \\ \\ \to S.I (1)= \frac{p}{2} \\ \\ \bold{For \: 7 \: years : } \\ \to S.I (2)= \frac{p \times r \times t}{100} \\ \\ \to S.I( 2)= \frac{p\times 5 \times 7}{100} \\ \\ \to S.I( 2)= \frac{7p}{20} \\ \\ \to S.I(1)- S.I(2) = 150 \\ \\ \to \frac{p}{2} - \frac{7P}{20} = 150 \\ \\ \to \frac{10p- 7p}{20} = 150 \\ \\ \to 3p = 3000 \\ \\ \bold{\to p = 1000 \: rupees}$