When x is added to each of the number 7, 11, 18 and 23, then the number so obtained are in proportion. What is the mean proportional between (x - 1) and (2x - 10)?
Show answer & explanation
Correct answer: D
Explanation
The correct answer is option 4 i.e. 48.
Let's solve the problem step-by-step.
When x is added to each number, the numbers become: 7 + x, 11 + x, 18 + x, and 23 + x
These numbers are in proportion, so we can set up the equation:
(7 + x) / (11 + x) = (18 + x) / (23 + x)
Cross-multiplying gives:
⇒ (7 + x)(23 + x) = (11 + x)(18 + x)
⇒ 161 + 30x + x = 198 + 29x + x
⇒ x = 37
The mean proportional between (x - 1) and (2x - 10) is the square root of their product:
⇒ Mean Proportional = √((x - 1)(2x - 10))
⇒ Substituting x = 37:
⇒ Mean Proportional = √((37 - 1)(2 × 37 - 10)) = √(36 × 64) = √(2304) = 48
Therefore, the mean proportional between (x - 1) and (2x - 10) is 48.