Question

A sum of money lent out at simple interest amount to rupees 2520 in 2 years and to rupees 2700 in 5 years. Find the sum of money and the rate of interest.

Answer 1

Let the sum of money be ₹ P and the rate of interest be R%

Amount (A)= principal (P) +S. Interest (S.I)

Amount for 2 years= ₹2520

Amount for 5 years= ₹2700

Simple interest for 3 years= 2700-2520= 180

Simple interest for 1 year= 180/3= 60

Simple interest for 2 years = 60×2= ₹120

Principal = amount -simple interest

P = A-P

P = 2520 - 120

P = ₹ 2400

Rate (R) =( S.I × 100)/ P × T

R= (120 × 100)/2400× 2

R= 60 /24 = 5/2

R= 5/2= 2.5 %

Hence, the sum of money is ₹2400 and the rate of interest is 2.5%

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Hope this will help you.....

Answer 2

Solution :-

Let the principal be Rs. P and the rate of interest be R %

Given - Sum of money lent out at simple interest amount to rupees 2520 in 2 years and to rupees 2700 in 5 years. 

Then, simple interest for 3 years = 2700 - 2520

= Rs. 180

Simple interest for 1 year = 180/3

= Rs. 60

Simple interest for first 2 years = Rs. 60*2

= Rs. 120

Amount (After 2 years) = Principal + Simple Interest

2520 = P + 120

⇒ P = 2520 - 120

⇒ P = 2400

So, the Principal is Rs. 2400

Now, Rate of Interest -

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


⇒ 120 = (2400*R*2)/100

⇒ 120 = 48R

⇒ R = 120/48

⇒ R = 2.5 %

So, Rate of Interest is 2.5 %

Answer.