Raj invested 10000 in a fund. at the end of first year, he incurred a loss but his balance was more than 5000. this balance, when invested for another year, grew and the percentage of growth in the second year was five times the percentage of loss in the first year. if the gain of Raj from the init…

Question

Raj invested 10000 in a fund. at the end of first year, he incurred a loss but his balance was more than 5000. this balance, when invested for another year, grew and the percentage of growth in the second year was five times the percentage of loss in the first year. if the gain of Raj from the initial investment over the two years period is 35% then the percentage of loss in the first year is

Shreedhar Goyal · Answer

Let loss be x% in first yearBalance = (100-x)*10000/100 = (100-x)*100 > 5000 {Given}In 2nd year : percentage of growth = 5*xTherefore its amount = [(100+5*x)/100] * [(100-x)*100] = (100+5*x)(100-x)Overall growth over 2 years : 35% Therefore amount = 1.35 * 10000 = 13500 = (100+5*x)(100-x)Solving:13500 = 10000 + 400*x - 5*x^23500 = 400*x - 5*x^2700 = 80*x - x^2x^2 - 80*x + 700 = 0x = 10, 70But (100-x)*100 > 5000 {Given}...Therefore x = 10 only

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