Eight Standard >> Simple interest | Part-2

Example 1: At what time will a sum of money be treble itself at 10% per annum simple interest?

Solution:
 Let sum of money P=Rs   \(x\)
  Amount(A)=  \(3x\), I=A-P=  \(3x-x=2x\)
  R=10% p.a
  I=\(\frac{PRT}{100}\)
  \(\therefore\ 2x=x \times \frac{10}{100}\times T\)
           =20

Required time is 20 years.

Example 2: At what rate a sum of money amounts to Rs 5400 in 3 years and Rs 6000 in 5 years?

Solution:
    Let the principal amount is Rs P.
    Interest in each year is Rs I.

So for the first 3 years 
      P+3I=5400..(1)
     for first 5 years 
      P+5I=6000..(2)
Subtract (2) from (1) we get
  P+5I-P-3I=6000-5400
\(\Rightarrow 2I=600\)
\(\therefore\  I=\frac{600}{2}=300\)

 Put I=300 in equation (1)

  \(P+3\times 300=5400\)
\(\Rightarrow\ P+900=5400\)
\(\therefore\ P=5400-900\)
       =Rs 4500

\(\therefore\) Rate=\(\frac{100I}{P \times T}\)=\(\frac{100\times 900}{4500 \times 3}\)=\(\frac{20}{3}\)

\(\therefore\) required rate is \(\frac{20}{3}\)%  per annum.

Example 3: If the rate of interest increases from 5.5% to 6%, the interest on the sum deposited by a person increases by Rs 99 in 2 years. Find the sum.

Solution:
    Let the principle be Rs \(x\)
The interest on Rs \(x\) for 2 years at 5.5% per annum
  =Rs \(\frac{x \times 5.5 \times 2}{100}\)
  =Rs \(\frac{11x}{100}\)
Again, the interest on Rs x for 2 ears at 6% per annum
   =Rs \(\frac{x \times 6 \times 2}{100}\)
   =Rs \(\frac{12x}{100}\)

As pr question, we can write
   \(\frac{12x}{100}-\frac{11x}{100}=99\)
   \(\Rightarrow\ \frac{x}{100}=99\)
   \(\therefore\ x=99 \times 100\)
        =Rs 9900

\(\therefore\) required sum=Rs 9900.