Question
A shopkeeper buys a total of 27 items, consisting of tables
and chairs. The cost price ratio of one table to one chair is 20:9. Each table is sold at a 25% profit, while each chair is sold at a 25% loss. If the overall profit percentage on the entire transaction is 7%, how many chairs did the shopkeeper sell?Solution
Let number of tables and chairs sold is 'x' and '27 - x' respectively.
Let CP of 1 table and 1 chair is 20a and 9a respectively.
CP of 'x' tables = x * 20a = 20ax
CP of '27 - x' chairs = (27 - x) * 9a = (243 - 9x)a
SP of 'x' tables = 125% of 20ax = 25ax
SP of '27 - x' chairs = 75% of (243 - 9x)a = (182.25 - 6.75x)a
According to the question:
25ax + (182.25 - 6.75x)a = 107% of [20ax + (243 - 9x)a]
25x + 182.25 - 6.75x = 21.4x + 260.01 - 9.63x
6.48x = 77.76
x = 12
Total chairs sold = 27 - x = 15
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