Question

A certain amount earns simple interest of Rs. 1750 after 7 years. Had the interest been $2\% $ more, how much more interest would it have earned?
A.Rs. 35
B.Rs. 245
C.Rs. 350
D.Cannot be determined.

Answer 1

Hint: Here, we will be using the simple interest formula to find an equation with the given and by using the simple interest formula again for the rate of interest which is increased, we will get another equation. By solving these equations, we will get the required answer. Simple interest is defined as the interest calculated for the principal at a rate for a period of time.

Formula Used:
Simple Interest is given by the formula $S.I. = \dfrac{{P \times n \times r}}{{100}}$ where $S.I$ is the Simple Interest, $P$ is the principal, $r$ is the rate of Interest and $n$ is the number of years.

Complete step-by-step answer:
We are given that a certain amount earns simple interest of Rs. 1750 after 7 years.
Let \[x\] be the principal amount that earns a simple interest of Rs. 1750 after 7 years and $r$ be the rate of interest.
Now substituting $P = x$, $n = 7{\text{years}}$ and $S.I. = {\text{Rs}}.1750$ in the formula $S.I. = \dfrac{{P \times n \times r}}{{100}}$, we get
$1750 = \dfrac{{x \times 7 \times r}}{{100}}$
By cross-multiplying the term, we get
$ \Rightarrow 175000 = x \times 7 \times r$
Dividing both side by 7, we get
$ \Rightarrow xr = \dfrac{{175000}}{7}$
Now, we will find the interest earned if the rate of interest is \[2\%\] more by using the simple interest formula
Substituting $P = x$, $r = \left( {r + 2} \right)$, $n = 7{\text{years}}$ in the formula $S.I. = \dfrac{{P \times n \times r}}{{100}}$, we get
$S.I. = \dfrac{{x \times 7 \times \left( {r + 2} \right)}}{{100}}$
By multiplying the terms, we get
$ \Rightarrow S.I. = \dfrac{{7x \times \left( {r + 2} \right)}}{{100}}$
$ \Rightarrow S.I. = \dfrac{{7xr + 14x}}{{100}}$
Substituting $xr = \dfrac{{175000}}{7}$ in the above equation, we get
$ \Rightarrow S.I. = \dfrac{{7\left( {25000} \right) + 14x}}{{100}}$
Multiplying 7 by 25000, we get
$ \Rightarrow S.I. = \dfrac{{175000 + 14x}}{{100}}$
By simplifying the terms, we get
$ \Rightarrow S.I. = \dfrac{{175000}}{{100}} + \dfrac{{14x}}{{100}}$
$ \Rightarrow S.I. = 1750 + \dfrac{7}{{50}}x$
So, it is impossible to find the interest earned without the principal amount.
Therefore, the interest earned if the rate of interest is \[2\%\] more cannot be determined without the principal amount.
Thus Option (D) is the correct answer.

Note: We should remember that only with the principal amount, rate of interest, and number of years we can find the Simple Interest. We should have at least two of these terms known along with the simple interest to find the third term. Alternatively, we should have at least two equations with the same parameters to solve the equation and find the terms which are not unknown. We are given only the number of years and the principal and the rate of interest is not known, so we cannot determine the interest without knowing the principal amount.