Question

Find the time in which $2000 $ will amount to ₹ $2330 $at $11\% $p.a.

Answer 1

Hint: Here, principal rate, selling interest and rate are given in the question. The formula to find the selling price is equal to the subtraction of principal amount from changed principal amount. Then we will determine the time taken.

Complete step-by-step answer:
Principal rate is equal to ₹ $2000 $.
The changed principal amount ₹ $2330 $.
The selling price is not known.
The word formula to find the selling interest is equal to the subtraction of principal amount from principal amount.
We know the formula to find the selling price is,
 ${\rm{SI = changed amount - principal amount}} $
If we substitute the value for the changed amount and the value for the principal amount. Then we obtain,
 $\begin{array}{c}
{\rm{SI}} = 2330 - 2000\\
 = 330
\end{array} $ $ $
Our main aim is to show that the time in which ₹ $2000 $ will amount to ₹ $2330 $ at $11\% $p.a.
The required formula to find the time is equal to the ratio of product of selling interest as well as $100 $and principal as well as rate.
We know the formula to find the time which is given by,
 ${\rm{time}} = \dfrac{{{\rm{selling interest}} \times 100}}{{{\rm{principal}} \times {\rm{rate}}}} $
Now substitute the values of principal amount and selling interest which we have found earlier and finally substitute the value of rate, now we obtain
 ${\rm{time}} = \dfrac{{330 \times 100}}{{2000 \times 11}} $
By dividing all the divisible terms, we get time as,
 ${\rm{time}} = \dfrac{3}{2}{\rm{ years}} $
Therefore, the total time taken to amount ₹ $2000 $ to $2330 $ is $1.5{\rm{ years}} $.

Note: In this question, do not forget to subtract the principal amount from the new amount. This problem can be found directly that is the direct formula to find time is $\dfrac{{\left( {{\rm{new amount - principal amount}}} \right) \times {\rm{100}}}}{{{\rm{principle amount }} \times {\rm{ rate}}}} $