Question:
What least number must be subtracted from each of the numbers 14, 17, 34 and 42 so that the remainders are proportional ?
What least number must be subtracted from each of the numbers 14, 17, 34 and 42 so that the remainders are proportional ?
Updated On: Oct 3, 2024
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The Correct Option is C
Solution and Explanation
Let's Assume the subtracted number be \(x\)
From the question = \(\frac{14 - x}{17 - x} = \frac{34 - x}{42 - x}\)
= \((14 - x)(42 - x) = (34 - x)(17 - x)\)
= \(588 - 14x - 42x + x^2 = 578 - 34x - 17x + x^2\)
= \(588 - 56x = 578 - 51x\)
= \(- 56x + (-51x) = 578 - 588\)
= \(- 5x = -10 \)
\(x = \frac{10}{5}\)
\(x = 2\)
The correct option is (C): 2
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