A certain sum in certain time becomes Rs. 500 at the rate of 8% per annum S.I and the same sum amounts to Rs. 200 at the rate of 2% S.I in…

50 years

NA

Solution:

Formula: S.I = P n r /100 where,

P = Principal amount

n = time duration in years

r = rate of interest

Given :

1st case: At 8% the principal is increased to Rs.500.

So, S.I = (500 - P)

2nd case: At 2% the same principal ranges to Rs.200.

So,S.I = (200 - P) and the time duration is equal in both the cases.

1st case : (500 - P) = P n (8)/100

So, P = 100(500 - P) /8n ------> 1

2nd case: (200 - P) = P n (2)/100

So, P = 100(200 - P) /2n -------> 2

Equating 1 and 2 we get

100(500 - P) /8n = 100(200 - P) /2n

(500 - P)/4 = (200 - P)

500 - P = 800 - 4P

4P - P = 800 - 500

3P = 300

P = 300/3

P = 100

So 1 => 100 = 100(500 - 100) / 8n

1 = 400/8n

8n = 400

n = 400/8

n = 50 years

So, the correct option is B). 50 years