Question

A certain sum of money amounts to rs.1300 in 2 years and to rs. 1525 in 3.5 years. find the sum and the rate of interest.

Answer 1

let sum be x
& rate be y
then
x(1+2y/100)=1300
or x=130000/(100+2y)..............(1)
again
x(1+3.5y/100)=1525
or x=1525000/(1000+35y)
then
130000/(100+2y)=1525000/(1000+35y)
or 130(1000+35y)=1525(100+2y)
or 130000+4550y=152500+3050y
or 1500y=22500
or y=225/15=15......…......(ans)
putting the value of y in (1)
x=130000/(100+30)
or x=1000........ ...(ans)

Answer 2

Scenario 1:

Final amount = Rs.1300

No. of years of deposit = 2

Scenario 2:

Final amount = Rs.1525

No. of years of deposit = 3.5

Let us find the difference in Final amount and the no. of years of deposit.

1525 - 1300 = 225

Years of deposit 3.5-2 = 1.5

Rs.225 interest for 1.5 years

Therefore, for one year, the interest will be  225 / 1.5= Rs.150

So, for 2 years, the interest will be  150 * 2 = Rs. 300

Principal = Final amount - Interest = 1300-300

Sum of money (Principal) = Rs.1000.

We know, Simple Interest = PNR/100

R = (SI * 100) / (P * N)

= 300* 100 / 1000 * 2  

Rate of interest = 15%