A certain sum of money amounts to ₹ 720 in 2 years and ₹ 870 in 4.5 years. Find the sum and the rate of interest.

600, 10%

NA

Solution:

Formula: Interest = Amount - Principal and

Interest = Pnr / 100 where,

P = Principal, n = number of years , r = rate of interest in percentage

1st case: Amount = Rs.720 in 2 years

So, (P×2×r)/100 = 720 - P

(P×r)/50 = 720 - P

Pr = 36000 - 50P

r =( 36000 - 50P )/P

2nd case:Amount = Rs.870 in 4.5 years

So, (P×4.5×r)/100 = 870 - P

(P×4.5×r) = 87000 - 100P

Pr = (87000 - 100P )/4.5

Since r =( 36000 - 50P )/P we have

(36000 - 50P) = (87000 - 100P )/4.5

4.5 × (36000 - 50P) = (87000 - 100P )

162000 - 225P = 87000 - 100P

225P - 100P = 162000 - 87000

125P = 75000

P = 75000/125

P = Rs. 600

r =( 36000 - 50×600 )/600

r =( 36000 - 30000 )/600

r =6000/600

r = 10%

So, the correct option is A). 600, 10%