The sum of three numbers is 172. The ratio of the first and second numbers is 8:11. The ratio of the second and third is 5:7. Find the second number.
Correct answer: B. 55
- A. 44
- B. 55
- C. 66
- D. 77
Explanation
Make the second term common: 8:11 becomes 40:55, while 5:7 becomes 55:77. Thus the three numbers are 40k, 55k and 77k, so 172k = 172 and the second number is 55. The likely mistake is choosing 44 by treating the ratios as directly compatible without first equalising the common term.
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About Ratio and Proportion
Ratios compare quantities in the same units, while proportions state that two ratios are equal. Problems cover simplification, division in a given ratio, direct and inverse variation, scale, and missing terms, with attention to the difference between a ratio and a fraction representing part of a whole.
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