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ICSE Class 8 Answered

Two equal sums of money were lent at simple interest at 11%p.a for3  1/2 years and 4  1/2 years respectively. If the difference in intrstest for two. Periods was ₹412.50, find each sum.
Asked by ovirucha | 17 Feb, 2015, 09:13: PM
answered-by-expert Expert Answer

Let x be the principal that is taken on interest.

Rate of Interest = 11%

Simple Interest for 3 1 half years = begin mathsize 12px style fraction numerator P R T over denominator 100 end fraction end style = begin mathsize 12px style fraction numerator x space cross times space 11 space cross times space 7 over denominator 100 space cross times space 2 end fraction space equals space fraction numerator 77 x over denominator 200 end fraction end style .....(1)

Simple Interest for 4 1 halfyears = begin mathsize 12px style fraction numerator P R T over denominator 100 end fraction end style=begin mathsize 12px style fraction numerator x space cross times space 11 space cross times space 9 over denominator 100 space cross times space 2 end fraction space equals space fraction numerator 99 x over denominator 2 end fraction end style ... (2)

Difference in interest = 412.50

begin mathsize 12px style fraction numerator 99 x over denominator 200 end fraction space minus space fraction numerator 77 x over denominator 200 end fraction space space equals space 412.50 therefore space fraction numerator 99 x over denominator 200 end fraction space minus space fraction numerator 77 x over denominator 200 end fraction space space equals fraction numerator space 41250 over denominator 100 end fraction therefore space fraction numerator 99 x space minus space 77 x over denominator 200 end fraction space equals space fraction numerator space 41250 over denominator 100 end fraction therefore space fraction numerator 22 x over denominator 2 end fraction equals space 41250 therefore space 11 x space equals space 41250 therefore space x space equals space 3750 end style

Hence the principal amount that was lent on interest is Rs. 3750

Answered by Mili Hariyani | 18 Feb, 2015, 10:58: AM

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