Profit and Loss

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Ex. 20. The price of a jewel, passing through three hands, rises on the whole by 65%. If the first and the second sellers carned 20% and 25% profit respectively, find the percentage profit earned by the third seller.

Sol. Let the original price of the jewel be Rs. P and let the profit earned by the third seller be x%. Then, (100 + x)% of 125% of 120% of of P P = 165% Rightarrow [(100 + x)/100 * 125/100 * 120/100 * P] = (165/100 * P) Rightarrow (100 + x) = ((165 * 100 * 100)/(125 * 120)) =110 Rightarrow x=10\%. -

On one he gains 16% while on the other he loses 16%. How much does he gain or lose in the whole transaction?

Sol. Remember: In such a case, there is always a loss. The selling price is immaterial. Loss% = Common Loss and Gain%2 16 10 10 2 64 % = 2:56%. 25

Ex. 22. A dealer sold three-fourth of his articles at a gain of 20% and the remaining at cost price. Find the gain earned by him in the whole transaction.

Sol. Let C.P. of whole be Rs. x. C.P. of Total 3 4 th=Rs. 3x 4 ,C.P. of * 1/4 * th =Rs. x 4 S.P.=Rs. [(120% * of * (3x)/4) + x/4] =Rs.( 9x 10 + x 4 )=Rs. 23x 20 . Gain Rs. Gain% = (2-x)= 20 (x-x100)% = 15%. 20

Ex. 23. A man bought a horse and a carriage for Rs. 3000. He sold the horse at a gain of 20% and the carriage at a loss of 10%, thereby gaining 2% on the whole. Find the cost of the horse.

(Μ.Β.Α. 2002).

Sol. Let the C.P. of the horse be Rs..x. Then, C.P. of the carriage Rs. (3000 - x). 20% of x + (- 10)% * 1 of (3000 - x) = 2% of 3000 Rightarrow x 5 - (3000 - x)/10 Rightarrow60 Rightarrow2x-3000+x=600 Rightarrow..3x=3600 Rightarrow hat x =1200.

Hence, C.P. Ex. 24. Find the single discount equivalent to a series discount of 20%, 10% and 5%.

Sol. Let marked price be Rs. 100. Then, Net S.F.= 95% of 90% of 80% of Rs. 100 Rs. Required discount = (100 - 68.4)% = 31.6% . 95 90 80x100 100 100100 100 Rs. 68.40.

Ex. 25. After getting two successive discounts, a shirt with a list price of Rs. 150 is available at Rs. 105. If the second discount is 12.5%, find the first discount.

Sol. Let the first, discount be x%. % of (100x)% of 150 = 105 Rightarrow 87.5 100 * (100-x) 100 *150=105 Rightarrow 100 - x = ((105 * 100 * 100)/(150 * 875)) = 80 Rightarrow x = (100 - 80) = 20 . First discount .

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