Question

Neha and Priya borrowed Rs. 5400 and Rs. 6000 respectively at the same rate of interest for $1\dfrac{3}{5}$ years. If Priya pairs Rs. 240 more than Neha, then find the rate of interest.

Answer 1

Hint: Since nothing is said about the form of interest, take it to be simple interest. Compute interest for both of them and compare them as per the constraints set by the question and then find out the rate of interest.

Formulas used:
$SI = \dfrac{{P \cdot R \cdot T}}{{100}}$ where SI is simple interest, P is the principal, R is the rate of interest and T is time for which loan is borrowed.

Complete step by step solution:
Here, first of all, we need to find out the simple interest of both parties and then solve for the rate of interest.
So, for Neha
$\
  S{I_{Neha}} = \dfrac{{{P_{Neha}} \cdot R \cdot T}}{{100}} \\
   = \dfrac{{5400 \times R \times T}}{{100}} \\
   = 54RT \\
\ $
For Priya it will be
$\
  S{I_{\Pr iya}} = \dfrac{{{P_{\Pr iya}} \cdot R \cdot T}}{{100}} \\
   = \dfrac{{6000 \times R \times T}}{{100}} \\
   = 60RT \\
\ $
Now we have both the simple interest paid by Priya and the one paid by Neha. From the question we know that Priya paid Rs. 240 more than Neha so if we add Rs. 240 in the simple interest paid by Neha, then both will be equal.
$\
  S{I_{\Pr iya}} = S{I_{Neha}} + 240 \\
  60RT = 54RT + 240 \\
\ $
Now we subtract 54RT from both sides and we end up with
\[\
  60RT = 54RT + 240 \\
  60RT - 54RT = 240 \\
  6RT = 240 \\
  RT = 40 \\
\ \]
But we know that
$\
  T = 1\dfrac{3}{5} \\
   = \dfrac{8}{5} \\
\ $
So, solving for R,
\[\
  RT = 40 \\
  R \times \dfrac{8}{5} = 40 \\
  R = \dfrac{{40 \times 5}}{8} \\
  R = 5 \times 5 \\
   = 25 \\
\ \]

Thus, in this question, the rate of interest is 25 percent.

Note:
In this question, we left time in the form of T as it is for as long as possible. This was done because time for both the girls was the same and so computing it in such a way was much easier than solving the whole thing in the beginning. In competitive exams, this very technique can mean the difference between solving the question or leaving it to save time for other questions due to lengthy calculations.