View source for Banking difficult problem solution

The difference between compound and simple interest on a certain sum for 2 years is 7½ % per annum is Rs 360. Find the sum .Verify the answer.<br>
*'''Interpretation of the problem: '''<br> 
1.Knowledge of the difference between compound and simple interest.<br>
2.Knowledge of the  formula's for  compound and simple interest.<br>
3.Identifing the terms giving in the problem.<br>
*'''Different approches to solve the problem:'''<br> 
1.using formula.<br>
*'''Concept used:'''
identifing the values from the given data.
R=7½% ,  n-2 years<br>
Assumping that principal  P=Rs 100.<math>Insert formula here</math>
Identifing the suitable formula, i.e A=P<br>
<math>S.I=PTR/100</math> <br>                                        
Substitution:  consider <math>S.I=PTR/100</math>( sustitute the values)<br>
<math> S.I= {\frac{100X 2 X 15}{2 X 100}} </math>       ( on simplification)<br>
''' S.I = Rs 15.'''<br>
With compound interest  ;<math>A=P[1+{\frac{R}{100}}]^n</math> <br>
A =<math> 100[{\frac{200+15}{200}}]^2</math><br>
=<math>100[{\frac{215}{200}}]^2</math>100<br>
=<math>100 X {\frac{215}{200}}X{\frac{215}{200}}</math><br>
'''A=  Rs 115.562'''<br>
'''C.I''' = Rs 115.562- 100<br>
'''C.I = Rs 15.562'''<br>
The difference in C.I and S.I is Rs 0.56<br>
The difference in C.I and S.I is Rs 0.56 when principal=Rs 100.<br>
If the difference in C.I and S.I is Rs 360, principal = x 360 = Rs 64285.<br>
'''Verification''' :<br>
<math>S.I={\frac{PTR}{100}}</math> <br> 
<math>S.I={\frac{64285 X 2 X 7.5}{100}}</math> <br>   = ''' Rs 9642.75'''
<math>A=P[1+{\frac{R}{100}}]^n</math><br>        
A=P= 64285[1+{\frec}{7.5}{100}}]^2=''' 74289.3'''<br>
'''C.I = A – P'''<br>
= 74289.3- 64285<br>
= 10004.3 Rs<br> 
'''Therefore the difference between C.I and S.I is = Rs 360.'''
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