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A firm ordered 15 premium machines and some standard machines. The price of a premium machine was 6 times that of a standard machine. By mistake, the number of premium and standard machines was interchanged in the delivery, which increased the total bill by 62.5%. What was the ratio of the number of premium machines to standard machines in the original order?

1. 3:7
2. 4:9
3. 1:2
4. 2:5

Correct answer: 1:2

Solution

Let standard machines be $x$ and premium machines be 15. If prices are 1 and 6 respectively, original bill = $15\cdot 6 + x = 90+x$. After interchange, bill = $x\cdot 6 + 15 = 6x+15$. Given the increase is 62.5%, so $6x+15 = 1.625(90+x)$, which gives $x=30$, hence ratio premium:standard = $15:30=1:2$.

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