Question

When x is added to each of 9, 15, 21 and 31, the numbers so obtained are in proportion. What is the mean proportional between the numbers (3x - 2) and (5x + 4)?
1. 30
2. 42
3. 35
4. 20

Answer 1

Correct Answer - Option 3 : 35

Given-

When x is added to each of 9, 15, 21 and 31, the numbers so obtained are in proportion.

Concept Used-

If a, b, c and d are in proportion, then a/b = c/d

Mean proportion of two numbers a and b is √ab

Calculation- 

According to Question-

(9 + x)/(15 + x) = (21 + x)/(31 + x)

⇒ (9 + x)(31 + x) = (15 + x)(21 + x)

⇒ x² + 40x + 279 = x² + 36x + 315

⇒ 4x = 36

⇒ x = 9

Mean proportion of (3x - 2) and (5x + 4) = √{(3×9 - 2)(5×9 + 4)}

⇒ √(25 × 49)

⇒ 35 

∴ Mean proportional between the numbers (3x - 2) and (5x + 4) is 35.