Which of the following numbers must be added to each of the numbers 9, 16, 13 and 23 so that the resulting numbers are in proportion?
Show answer & explanation
Correct answer: C
Explanation
The correct answer is option 3 i.e. .
Let the number to be added be x.
The numbers after adding x are: (9 + x), (16 + x), (13 + x), (23 + x).
They are in proportion, so:
(9 + x) / (16 + x) = (13 + x) / (23 + x)
Cross-multiply:
(9 + x)(23 + x) = (16 + x)(13 + x)
Expand:
(9×23) + 9x + 23x + x² = (16×13) + 16x + 13x + x²
207 + 32x + x² = 208 + 29x + x²
x² cancels out:
207 + 32x = 208 + 29x
32x - 29x = 208 - 207
3x = 1
x = 1/3