Question

If Rs. 750 amounts to Rs. 885 in three years at simple interest, what will Rs. 1200 amounts to in $3\dfrac{1}{2}$ years? (The rate is the same in both cases)

Answer 1

Hint: First find the interest by subtracting the principal from the amount. After that use the formula of simple interest, $I = \dfrac{{PRT}}{{100}}$ to find the rate of interest. Then use the rate of interest and other values to find the interest by the formula of simple interest. After that add the interest value to the principal to get the amount.

Complete step-by-step solution:
Let the rate of the interest be $R$and the amount on Rs. 1200 be $A$.
Simple interest is given by the formula:
$I = \dfrac{{P \times R \times T}}{{100}}$
Where P is the principal amount,
R is the rate of the interest,
T is the time,
I is Simple Interest.
For interest value, subtract the principal from the amount,
$ \Rightarrow 885 - 750 = 135$
Here,
Principal, $P = 750$
Interest, $I = 135$
Time, $T = 3$
Now, by substituting these values in the above simple interest formula we get,
$ \Rightarrow 135 = \dfrac{{750 \times R \times 3}}{{100}}$
Multiply both sides by 100,
$ \Rightarrow 750 \times R \times 3 = 135 \times 100$
Multiply the terms on both sides,
$ \Rightarrow 2250R = 13500$
Divide both sides by $2250$,
$ \Rightarrow R = \dfrac{{13500}}{{2250}}$
Cancel out the common factors,
$ \Rightarrow R = 6\% $
Now use the rate of interest to find the interest amount on Rs. 1200,
Here
Principal, $P = 1200$
Rate of Interest, $R = 6\% $
Time, $T = 3\dfrac{1}{2} = \dfrac{7}{2}$
Substitute the values in simple interest formula,
$ \Rightarrow I = \dfrac{{1200 \times 6 \times \dfrac{7}{2}}}{{100}}$
Cancel out the common factors,
$ \Rightarrow I = 6 \times 6 \times 7$
Multiply the terms,
$ \Rightarrow I = 252$
We know that the amount is the summation of the principal value and interest value,
$ \Rightarrow A = P + I$
Substitute the values,
$ \Rightarrow A = 1200 + 252$
Add the terms,
$\therefore A = 1452$

Hence, the amount will be Rs. 1452.

Note: The students might make mistakes by not subtracting the principal value from the amount to get the interest value. It will lead to getting the wrong rate of interest and the amount of Rs. 1200.
Students must know that time, sometimes it is given in days, sometimes in months, and sometimes in years. So, always convert time into a year as the value of T in the formula is corresponding to the year, for 1-year take \[T = 1\] but for 6 months take \[T = \dfrac{1}{2}\] and accordingly.