Question
Download Solution PDFWhich smallest positive number should be subtracted from each 9 and 13 so that 18 is the third proportion of them?
Answer (Detailed Solution Below)
Detailed Solution
Download Solution PDFGiven:
18 is the third proportion.
Concept used:
1. If A : B :: C : D then (B × C) = (A × D)
2. (a - b)2 = a2 - 2ab + b2
Calculation:
Let the smallest positive number be Q.
The proportion becomes (9 - Q) : (13 - Q) : : (13 - Q) : 18.
According to the question,
(13 - Q)2 = (9 - Q) × 18
⇒ 169 + Q2 - 26Q = 162 - 18Q
⇒ Q2 - 8Q + 7 = 0
⇒ (Q - 7)(Q - 1) = 0
So, the smallest number = Q = 1
∴ The smallest number is 1.
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