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