1. An equal sum is invested in two different schemes. One scheme gives simple interest and the other gives compound interest (annual compounding). The total interest obtained after 2 years from both the schemes together is Rs 2090. If both the schemes have 18% per annum interest rate, then what is the first year interest (in Rs) of simple interest scheme?
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By: anil on 05 May 2019 02.06 am
Let sum invested in both schemes = Rs. $$100x$$ Time period = 2 years and rate of interest in both schemes = 18% Total interest from both schemes = $$(frac{P imes R imes T}{100})+[P(1+frac{R}{100})^T-P]$$ => $$(frac{100x imes 18 imes 2}{100})+[100x(1+frac{18}{100})^2-100x]=2090$$ => $$(36x)+[100x(frac{118}{100})^2-100x]=2090$$ => $$36x+139.24x-100x=2090$$ => $$75.24x=2090$$ => $$x=frac{2090}{75.24}=27.78$$ $$ herefore$$ Simple interest in 1st year = $$frac{(100 imes27.78) imes18 imes1}{100}$$ = $$27.78 imes18=500.04approx Rs.$$ $$500$$ => Ans - (B)
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