Question
An officer ordered 3 computers of brand X and some
computers of brand Y. The price of one computer of brand X was thrice that of brand Y. When the order was executed, it was found that the numbers of the two brands has been interchanged. This increased the bill by 50%. Find the ratio of the number of brand X computers to that of brand Y computers in the original order was.Solution
Let the no of computers of brand Y = n and the cost of 1 computer of brand Y = Re. k Original cost of brand Y computer = Rs. kn and original cost of brand X computer = Rs. 3 x 3k = 9k Total original cost = Rs.(kn + 9k) In the case of executed order, Cost of brand X computer = Rs. 3kn And cost of brand Ycomputer = Rs. 3k Total cost of executive order = Rs. (3kn + 3k) As per the question, 150% of (kn+ 9k) = 3kn + 3k 150% of (n+ 9) = 3n + 3 ⇒ 150/100 x (n + 9) = 3n + 3 ⇒ 3/2 x (n + 9) = 3n + 3 ⇒ 1/2 x (n + 9) = n + 1 ⇒ n + 9 = 2n +2 ⇒ n = 7 Required ratio = 3 : 7
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