Question

The simple interest on a certain sum for 8 years at \[12\% \] per annum is Rs. 3120 more than the simple interest on the same sum for 5 years at \[14\% \] per annum. Find the sum.

Answer 1

Hint:
Here, we have to find the sum using the concept of Simple Interest. Simple Interest is the rate at which we lend money. We will assume the sum to be \[P\] and find the simple interest on the sum for 8years in terms of \[P\]. Then we will find the simple interest on that sum for 5 years in terms of \[P\]. We will use the condition given in the question and form an equation. We will simplify the equation to find the required answer.

Formula Used:
Simple Interest is given by the formula: \[S.I = \dfrac{{P \times r \times t}}{{100}}\] where \[P\] is the principal amount, \[r\] is the rate of interest, \[t\] is the number of years.

Complete step by step solution:
Let us assume the sum be\[P\].
We will now find the simple interest for 8 years and 5 years using the formula \[S.I = \dfrac{{P \times r \times t}}{{100}}\].
Simple Interest on a certain sum for 8 years at 12% per annum \[ = \dfrac{{P \times 12 \times 8}}{{100}}\]
Simple Interest on a certain sum for 5 years at 14% per annum \[ = \dfrac{{P \times 14 \times 5}}{{100}}\]
Now it is given that the simple interest on a certain sum for 8 years is Rs. 3120 more than the simple interest on the same sum for 5 years.
So, we will form an equation based on the above condition. Therefore, we get
\[\dfrac{{P \times 12 \times 8}}{{100}} = 3120 + \dfrac{{P \times 14 \times 5}}{{100}}\]
By taking LCM on right hand side of the equation, we get
\[ \Rightarrow \dfrac{{P \times 12 \times 8}}{{100}} = \dfrac{{312000 + P \times 14 \times 5}}{{100}}\]
Multiplying 100 on both the sides, we get
\[ \Rightarrow P \times 12 \times 8 = 312000 + P \times 14 \times 5\]
Multiplying the terms, we get
\[ \Rightarrow 96P = 312000 + 70P\]
Subtracting \[70P\] on both sides, we get
\[ \Rightarrow 96P - 70P = 312000\]
Subtracting the terms, we get
\[ \Rightarrow 26P = 312000\]
Dividing 312000 by \[26P\], we get
\[ \Rightarrow P = \dfrac{{312000}}{{26}}\]
\[ \Rightarrow P = 12000\]

Therefore, the principal amount is Rs. 12000.

Note:
Here, we have found out the sum which is known as Principal amount. Principal is the original sum of money loaned/deposited. Time is the duration for which the money is borrowed/deposited. Rate of Interest is the percent of interest that you pay for money borrowed, or earn for money deposited. We should know that the time has to be in the number of years and rate of interest in percentage.