Question

A certain sum becomes Rs. \[6400\] in \[4\] years and Rs. \[8200\] in \[7\] years at simple interest. Find the principal.

Answer 1

Hint: We know that, amount means the sum of principal and the simple interest for a certain year.
With the fact mentioned above we will find the interest of the year and with the help of the interest found we will find the required principal.

Complete step-by-step answer:
It is given that a certain sum becomes Rs. \[6400\] in \[4\] years and Rs. \[8200\] in \[7\] years at simple interest. We have to find the principal.
Let x be the principal and y be the interest of the principle.
Since sum is nothing but the addition of principal and interest, we have
Principal + interest of \[7\] years is Rs. \[8200\]
That is \[x + 7y = 8200\] … (1)
Principal + interest of \[4\] years is Rs. \[6400\]
That is \[x + 4y = 6400\] … (2)
Let us subtract equation (1) and (2) we get,
Interest of \[3\] years is Rs. \[(8200 - 6400) = Rs.1800\]
that is \[x + 7y - x - 4y = 8200 - 6400\]
which in turn implies\[3y = 1800\]
So, the interest of a year is \[Rs.\dfrac{{1800}}{3} = Rs.600\]
That is \[y = \dfrac{{1800}}{3} = 600\]
Therefore, interest for \[4\] years is \[Rs.(600 \times 4) = Rs.2400\]
That is \[4y = 2400\]
So, the principal is found by substituting the value of\[4y\]in equation (2), we get
\[x + 2400 = 6400\]
\[x = 4000\]
Hence, we have found the principal of the given relation as \[Rs.4000\].

Note: Without substituting the value of y in equation (2) we can substitute the value of y in equation (1) If we take the interest for \[7\] years we will get the same value for the principal.
Interest for \[7\] years is \[Rs.(600 \times 7) = Rs.4200\]
So, the principal is \[Rs.(8200 - 4200) = Rs.4000\]
Hence, the principal is \[Rs.4000\].