Question

Both Amar and Prem invested certain amount in a bank at a rate of interest of 5%.Interest at the end of the year will be accumulated into the principle amount.At the end of the first year,Amar withdraws 50% of the accumulated amount,while Prem withdraws 11,500 . At the end of the third year,Prem had an accumulated amount equal to that which Amar had at the end of the second year.Amar withdraws Rs 4050 at the end of the second year.The total interest earned by Amar is Rs 3,950 for 3 year.

a)What is the amount initially invested by Amar?

Answer 1

Amar invests an amount at a rate of interest of 5% and at the end of the first year Amar withdraws 50% of the accumulated amount.
Let us assume the amount invested by Amar is Rs.x.
Then by the formula, SI = (p * n * r) / 100.
Where, p = principal, n = number of years, r = rate of interest and,
SI = simple interest.
Here, p = x, r = 5%, and n = 1.
∴, SI = (x* 1 * 5) / 100=x/20
∴ the acumulated amount = Principal + SI=x + x/20=21x/20
Amar withdraws 50% at the end of the 1st year which is:21x/20×50/100
=21x/40
For the 2nd yr. he will invest Rs.(21x/20-21x/40)=21x/40 as he already withdrawn 50% of the accumulated amount.
For the 2nd yr., p = 21x/40, n = 1 year and r = 5%.
SI = (21x/40)* 1 * 5/ 100=21x/800
Accumulated amount = 21x/40+21x/800=441x/800
At the end of second year Amar withdraws Rs. 4,050
Remaining amount=441x/800 - 4050 =(441x-3240000)/800
Then for the 3rd yr., p = (441x-3240000)/800, n = 1 year and r = 5%.
SI = {(441x-3240000)/800} * 1 * 5) / 100=(441x-3240000)/16000
Accumulated amount = (441x-3240000)/800+(441x-3240000)/16000
Total interest earned by Amar is Rs.3,950/- for 3 years. 
∴, x/20+21x/800+(441x-3240000)/16000 = 3950.
or,(800x+420x+441x-3240000)/16000 =3950
or, 1661x-3240000=3950×16000
or, 1661x=63200000+3240000
or, 1661x=69440000
or, x=66440000/1661
or, x=40000
So the amount invested by Amar is Rs.40,000

Answer 2

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