Simple Interest Problem

[toponlinetool]

Please guide me to solve the following simple interest problem.
A sum becomes Rs. 3000 at the rate of 12% per annum (simple interest). The same sum becomes Rs. 3300 at the rate of 15% per annum (simple interest) in the same duration. Find the sum and the duration.

Actually, i have used formula, Amount= Principle+Simple Interest, but getting confused due to two amounts, 3000 & 3300. Can anyone please help to get the answer?

 

[HallsofIvy]

You have two unknown values, "sum" and "duration", to solve for so you need two equations. You get those two equations from the two different situations.

Yes, "Amount= Principle+ Simple interest". Call the principle, here the "sum", in Rs, P, and the duration in years, t. At 12% per annum the total interest will be 0.12Pt so 3000= P+ 0.12Pt= (1+ 0.12t)P. At 15% per annum the total interest will be 0.15Pt so 3300= P+ 0.145Pt= (1+ 0.15t)P.

Solve the two equations (1+ 0.12t)P= 3000 and (1+ 0.15t)P= 3500 for P and t.

 

[toponlinetool]

You have two unknown values, "sum" and "duration", to solve for so you need two equations. You get those two equations from the two different situations.

Yes, "Amount= Principle+ Simple interest". Call the principle, here the "sum", in Rs, P, and the duration in years, t. At 12% per annum the total interest will be 0.12Pt so 3000= P+ 0.12Pt= (1+ 0.12t)P. At 15% per annum the total interest will be 0.15Pt so 3300= P+ 0.145Pt= (1+ 0.15t)P.

Solve the two equations (1+ 0.12t)P= 3000 and (1+ 0.15t)P= 3500 for P and t.

Thanks a lot.