Official Guide Explanation:
Problem Solving #130




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Solution and Metadata

Question: 130
Page: 78
Difficulty: 6 (Moderately Difficult)
Category 1: Word Problems > Work Problems > 2 inputs
Category 2: Arithmetic > Ratio and Proportion >

Explanation: To find the ratio of X's time to Y and Z's time, you need both of those quantities. X's time is given, so find Y and Z's time, working together. The time it takes for two machines to do a job, working together, is ((AB)/(A + B)), where A and B are the amounts of time it takes for the two machines to do the job independently. So, A = 15 and B = 18, so the time is ((15(18))/(15 + 18)) = ((3(5)(18))/(3(5 + 6))) = (90/11). The ratio, then, is ((X)/(Y&Z)) = (12/((90/11))) = 12((11/90)) = ((6(2)(11))/(6(15))) = (22/15), choice (D).

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