Question

A bookseller buys 1000 books from a publisher. He sells some books at the marked price of 24 ruppes each and disposes of the remaining books at sale price of 22.50 rupees each. If his total receipts from the sale of books are 23670 rupees , find how many books were sold at each price.

Answer 1

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total number of books purchased = 1000
let the number of books sold at 24 rupees be 'x'.
let the number of books sold at sale price of 22.50 rupees be 'y'.
according to the first condition ,
x + y = 1000. equation 1
according to the second condition,
24x + 22.50y = 23670. equation 2
multiplying equation 1 by 24
24x + 24y =24000. equation 3
subtracting 2 from 1 we get,
24x +24y = 24000
24x +22.50y =23670
(all signs changed to negative.)
0x. +1.5y =330
y = 330/1.5
y = 3300/15
(to remove the decimal point multiplying above and below by 10.)
y = 220 .
substitute y = 220 in equation 1 ,
x+ 220 = 1000
x = 1000 - 220
x = 780
therefore ,
number of books sold at 24 rupees are 780.
number of books sold at 22.50 rupees are 220.