Question

At what time will the sum rs. $1200$ amounts to rs. $1500$ at $6\dfrac{1}{2}$ per annum.

Answer 1

Hint: Here, first of all find the simple interest taking the difference between the principal and the amount and then will use the formula for simple interest and find the term period in years using the basic simplification of the mathematical expression.

Complete step by step answer:
Specify the given data:
Term period, $T = ?$
Sum, $P = Rs.1200$
Amount, $A = Rs.1500$
Rate of interest, $R = 6\dfrac{1}{2}$
Convert the above rate of interest in the form of simple fraction.
Rate of interest, $R = \dfrac{{13}}{2}$
Now, the simple interest is calculated by finding the difference of amount and the sum.
Simple Interest $I = A - P$
Place the given values in the above expression –
$I = 1500 - 1200$
Simplify finding the difference of the terms in above expression –
$I = 300$Rs.
Now, the simple interest can be given by the formula –
$I = \dfrac{{PRT}}{{100}}$
Place all the known terms in the above equation –
$300 = \dfrac{{1200 \times 13 \times T}}{{2 \times 100}}$
Make the required term “T” the subject and move all the terms in the above expression. When you do cross multiplication the terms in the denominator are multiplied with the numerator of the opposite side.
$T = \dfrac{{300 \times 100 \times 2}}{{1200 \times 13}}$
Simplify the above expression finding the removing the common factors from the numerator and the denominator.
$T = \dfrac{{300}}{{6 \times 13}}$
Again, find the common factors –
$T = \dfrac{{50}}{{13}}$years

Note: First of all remember the correlation equation of simple interest, amount and the principal. Always check the term period given or asked it can be years, months and in some rare cases days. Generally, the year in the simple interest formula is in terms of years only. Know the relation of converting the months to year for that you have to simply divide the months by twelve.