Question
Download Solution PDFWhen x is added to each of 26, 40, 22 and 34, then the numbers so obtained, in this order, are in proportion. Then, if 4x : y :: y : (7x-6), and y > 0, what is the value of y?
Answer (Detailed Solution Below)
Detailed Solution
Download Solution PDFGiven:
When x is added to each of 26, 40, 22, and 34, the numbers obtained are in proportion.
If 4x : y :: y : (7x - 6), and y > 0, find the value of y.
Formula used:
For numbers in proportion: \(\frac{a}{b} = \frac{c}{d}\)
For ratio: \(\frac{4x}{y} = \frac{y}{7x-6}\)
Calculation:
For the first condition:
The numbers after adding x: (26 + x), (40 + x), (22 + x), (34 + x).
Given these are in proportion:
⇒ \(\frac{26+x}{40+x} = \frac{22+x}{34+x}\)
⇒ (26 + x)(34 + x) = (40 + x)(22 + x)
⇒ 884 + 26x + 34x + x2 = 880 + 40x + 22x + x2
⇒ 884 + 60x = 880 + 62x
⇒ 4 = 2x
⇒ x = 2
For the second condition:
Given: \(\frac{4x}{y} = \frac{y}{7x-6}\)
Substitute x = 2:
⇒ \(\frac{4(2)}{y} = \frac{y}{7(2)-6}\)
⇒ \(\frac{8}{y} = \frac{y}{14-6}\)
⇒ \(\frac{8}{y} = \frac{y}{8}\)
⇒ 8 × 8 = y × y
⇒ y2 = 64
⇒ y = √64 = 8 (since y > 0)
∴ The correct answer is option (4).
Last updated on Jul 21, 2025
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