Question
The simple interest on a certain sum for 3 ½ years at 12% per annum is Rs. 98 more than the simple interest on the same sum for 2 ½ years at 14% per annum. Find the sum.
Hint:
Equate both the cases and then find the sum.
The correct answer is: P=Rs 1400
Complete step by step solution:
Let the sum of money = P
Case Ι
Principal amount = P, Rate = 12% and time = 3.5 years
We know the formula of Interest I = 
,
where P is Principal amount, T is number of years and is rate of interest
On substituting the values, we get 
…(i)
Case Ⅱ
Principal amount = P, Rate = 14% and time = 2.5 years
We know the formula of Interest I = ,
where P is Principal amount, T is number of years and is rate of interest
On substituting the values, we get 
…(ii)
It is given that the simple interest for case I is Rs 98 more than the simple interest for case Ⅱ.
So, 
On multiplying on both the sides, we get 7p = 9800
Divide the above equation by 7 on both the sides,
We get P = 1400
Hence the sum P = Rs 1400
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