Question

a certain sum amounts to Rs.73255 in 3 years and Rs 84525 in 5 years at simple interest. Find the sum.

Answer 1

Let P is the sum of amount , r is rate of interest and T is time
∴ SI = P × r × T/100

A/C to question,
73255 = P + SI in 3 years
73255 = P + P × r × 3/100 ------(1)

Similarly,
84525 = P + P × r × 5/100 ----(2)

Subtracting equation (1) from (2)
84525 - 73255 = P × r × (5 - 3)/100
11270 = 2Pr/100
5635 = Pr/100 -----(3), put it in equation (1)
73255 = P + 3 × 5635
P = 73255 - 16905
= 56350 RS

Hence, sum of amount is 56350 Rs

Answer 2

Solution :-

Simple interest after 3 years = Rs. 73255

Simple interest after 5 years = Rs. 84525

Simple interest for 2 years (i.e., 4th year and 5th year) = 84525 - 73255

= Rs. 11270

So, simple interest for 2 years is Rs. 11270

Simple interest for 1 year = Rs. 11270/2 = Rs. 5635

So, simple interest for 1 year = Rs. 5635

Then, Simple interest for 5 years = Rs. 5635*5 = Rs. 28175

P = Amount - Simple interest 

⇒ P = 84525 - 28175

Principal = Rs. 56350

So, initially the principal was Rs. 56350

Simple Interest = (P*R*T)/100

Simple interest for 5 years = Rs. 28175

Initial Principal = Rs. 56350

Time = 5 years

Rate of Interest = ?

⇒ 28175 = (56350*R*5)/100

⇒ 281750R = 2817500

⇒ R = 2817500/281750

⇒ R = 10 %

So, Principal Sum is Rs. 56350 and Rate of Interest is 10 %

Answer.