Three numbers are in a ratio 5 : 7: 9. If the difference between the largest and the smallest number is 20, find the middle number.
35
Since the three numbers are in the ratio \(5 : 7 : 9\), let them be \(5x\), \(7x\) and \(9x\) for some common multiplier \(x\).
The largest number is \(9x\) and the smallest is \(5x\), so their difference is \(9x - 5x = 4x\).
This difference is given as 20, so \(4x = 20\).
Solving gives \(x = \dfrac{20}{4} = 5\).
The middle number corresponds to the ratio term 7, so it equals \(7x = 7 \times 5 = 35\).
Key concept: introduce a single unknown multiplier for ratio quantities, use the given absolute condition to find it, then read off the required term.
Hence the middle number is 35.
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Important Questions from Ratio and Proportion
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