Ex.8.3 Q9 Compairing Quantities - NCERT Maths Class 7

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Question

Find the amount to be paid at the end of \(3\) years in each case:

(a)  Principal \(= \rm Rs\, 1,200\) at \(12\%\) p.a.

(b) Principal \(= \rm Rs\, 7,500\) at \(5\%\) p.a.

Text Solution

What is Known?

Principal, Time and the rate of interest.

What is Unknown?

Amount to be paid in three years.

Reasoning:

Simple interest can be calculated using the formula

Simple Interest 

\[\begin{align} & =\frac{\left[ \begin{align} & \text{Principal} \times  \text{Rate of interest} \\ &  \times  \text{Time (in years)} \\ \end{align} \right]}{\text{100}\ } \\ \end{align}\]

And amount is obtained by adding Principal to the interest

Steps:

(a) Principal = \(\rm Rs\, 1,200\) at \(12\%\) p.a.

Simple Interest 

\[\begin{align} & =\frac{\left[ \begin{align} & \text{Princial} \times  \text{Rate of interest} \\ &  \times \text{Time (in years)} \\ \end{align} \right]}{100} \\ & =\frac{1200 \times  12 \times  3}{100} \\ & =\text{Rs }432 \\ \end{align}\]

\[\begin{align}\text{Amount} &=\text{Principal + Interest }\\&= \text{Rs }1200 + \text{Rs }432 \\ &= \text{Rs }1632\end{align}\]

So, the amount to be paid after \(3\) years will be \(\rm Rs. \,1632\)

(b) Principal \(= \rm Rs \,7,500\) at \(5\%\) p.a.

Simple Interest 

\[\begin{align}& =\frac{\left[ \begin{align} & \text{Princial} \times  \text{Rate of interest} \\& \times  \text{Time (in years)} \\ \end{align} \right]}{100} \\ & =\frac{7500 \times  5 \times  3}{100}  \\ & =1125 \end{align}\]

\[\begin{align}\text{Amount} &= \text{Principal + Interest}\\&= 7500 +1125 \\&= 8625\end{align}\]

So, the amount to be paid after \(3\) years will be \(\rm Rs.\,8625\)