Miscellaneous Examples based on Simple Interest

                         Miscellaneous Examples based on Simple Interest

i) A sum of money lent at simple interest amounts to Rs 3224 in 2 years and 4160 in 5 years. Find the sum and the rate of interest.

Solution

Amount in 5 years = (principal SI for 5 years) = Rs 4160.
Amount in 2 years = (principal SI for 2 years) = 3224.
On subtracting we get :
SI for 3 years = Rs (4160 - 3224) = Rs 936.

Or SI for 2 years = Rs (936 x 2 / 3 ) = Rs 624.

Or sum = (amount for 2 years) - (SI for 2 years) = Rs (3224 - 624) = Rs 2600.

Now, principal = 2600, SI = Rs 624, time = 2 years.

Therefore, rate = (100 x SI)/(P x T) = (100 x 624) / (2600 x 2)% = 12% p.a.


ii)The simple interest on a certain sum for 3 years at 8% per annum is Rs 96 more than the simple interest on the same sum for 2 years at 9% per annum. Find the sum.

Solution

Let the required sum be Rs X. Then,
SI on Rs X at 8% per annum for 3 years = Rs (X x 8 x 3) / 100 = Rs 6X / 25.
SI on Rs X at 9% per annum for 2 years = Rs (X x 9 x 2) / 100 = Rs 9X / 50.
Now according to the question
(6X / 25) - (9X / 50 ) = 96
or (12X - 9X) / 50 = 96
or 3X =50 x 96
or X = (50 x 96) / 3 = 1600.
Hence, the required sum is Rs 1600.