1. A certain sum of money amounts to Rs 918 in 2 years and Rs 969 in 3.5 years at simple interest. What is the rate of interest (in %)?
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By: anil on 05 May 2019 01.47 am
Let sum of money = Rs. $$100x$$ and rate of interest = $$r\%$$ Amount under simple interest = $$P+frac{P imes r imes t}{100}$$ In 2 years, sum amounts to Rs. 918 => $$100x+frac{100x imes r imes 2}{100}=918$$ => $$100x+2rx=918$$ -----------(i) Similarly, after 3.5 years, => $$100x+frac{100x imes r imes 3.5}{100}=969$$ => $$100x+3.5rx=969$$ ------------(ii) Subtracting equation (i) from (ii), => $$1.5rx=969-918=51$$ => $$rx=frac{51}{1.5}=34$$ --------------(iii) Substituting it in equation (i), => $$100x=918-2(34)=850$$
=> $$x=frac{850}{100}=8.5$$ Substituting it in equation (iii), we get : $$r=frac{34}{8.5}=4\%$$ => Ans - (A)
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=> $$x=frac{850}{100}=8.5$$ Substituting it in equation (iii), we get : $$r=frac{34}{8.5}=4\%$$ => Ans - (A)