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  • A person bought 100 articles for Rs. 4000. He sold 20 of them at the gain of 5%. At what percent of the profit will sold the remaining articles so that he would gain 20% of profit in whole.

A person bought 100 articles for Rs. 4000. He sold 20 of them at the gain of 5%. At what percent of the profit will sold the remaining articles so that he would gain 20% of profit in whole.

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\ extGiven, \\ extCost of 100 articles = extRs. 4000 \ \ extTherefore, Cost price of 1 articles =frac4000100=mathrmRs .40 \\ extGiven that person sold 20 articles at a gain of 5 \%. \\ extCost of 20 articles =frac4000100 imes 20=operatornameRs .800 \\ extLet the selling price of 20 articles be Rs.x. \\ extTherefore, x =800+5 \% ext of 800 \\ mathrmx=800+frac5100 imes 800 Rightarrow x=800+40=840

\ extNow to get 20 \% ext gain on whole transaction, Selling price of all \\ extthe articles should be 120 \% extof cost price. \\ extLet the selling price of all the articles be Rs.y Therefore,\\ mathrmy=4000+20 \% ext of 4000 \\ mathrmy=4000+frac20100 imes 4000 \\ Rightarrow exty=4000+800=4800

\ extNow, Selling price of 80 articles =4800-840=mathrmRs .3960 \\ extCost price of 80 articles =40 imes 80= Rs. 3200 \\ extGain =3960-3200=mathrmRs. 760 \\ extTherefore, Gain \% ext on 80 articles =frac7603200 imes 100=23.75 \% \\ extHence person must sell the remaining articles at 23.75 \% ext gain.

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Deependra Verma

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