Question

If a number \( x \) be subtracted from each of the numbers 21, 38, 55, 106, then they become proportional. The value of \( x \) is:

• A. 1
• B. 2
• C. 3
• D. 4

Hint:

For proportionality equations, use the cross multiplication method and solve for the unknown variable.

Answer 1

The Correct Option is D

The given numbers: 21, 38, 55, 106 satisfy: \[ \frac{21 - x}{38 - x} = \frac{55 - x}{106 - x} \] Using cross multiplication: \[ (21 - x)(106 - x) = (38 - x)(55 - x) \] Expanding: \[ 2226 - 21x - 106x + x^2 = 2090 - 38x - 55x + x^2 \] Cancel \( x^2 \): \[ 2226 - 127x = 2090 - 93x \] Rearrange: \[ 136 = 34x \] \[ x = \frac{136}{34} = 4 \]
Thus, the correct answer is 4.