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Question

A trader bought a number of articles for Rs. 1,200. Ten were damaged and he sold each of the remaining articles at Rs. 2 more than what he paid for it, thus getting a profit of Rs. 60 on the whole transaction ?

Taking the number of articles he bought as x, form an equation in x and solve it.

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Solution

Number of articles bought by the trader = x
It is given that the trader bought the articles for Rs 1200.
S o space cos t space o f space o n e space a r t i c e space equals 1200 over x space R s T e n space a r t i c l e s space w e r e space d a m a g e d space. S o space n u m b e r space o f space a r t i c l e s space l e f t equals x minus 10 S e l l i n g space p r i c e space o f e a c h space o f space left parenthesis x minus 10 right parenthesis space a r t i c l e s equals open parentheses 1200 over x plus 2 close parentheses s e l l i n g space p r i c e space o f left parenthesis x minus 10 right parenthesis space a r t i c l e s space equals space left parenthesis x minus 10 right parenthesis space open parentheses 1200 over x plus 2 close parentheses P r o f i t space equals 60 left parenthesis x minus 10 right parenthesis open parentheses 1200 over x plus 2 close parentheses minus 1200 equals 60 1200 plus 2 x minus 12000 over x minus 20 minus 1200 equals 60 2 x minus 12000 over x minus 80 equals 0 2 x squared minus 80 x minus 12000 equals 0 x squared minus 40 x minus 6000 equals 0 x squared minus 100 x plus 60 x minus 6000 equals 0 x left parenthesis x minus 100 right parenthesis plus 60 left parenthesis x minus 100 right parenthesis equals 0 left parenthesis x minus 100 right parenthesis left parenthesis x plus 60 right parenthesis equals 0 x equals 100 comma negative 60
Number of articles cannot be negative. So, x = 100.


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