Question

The number that must be added to each of the numbers 8, 21, 13 and 31 to make the ratio of the first two numbers equal to the ratio of the last two numbers is

• A. 7
• B. 5
• C. 9
• D. None of these

Hint:

For ratio-based problems, set up proportion equations and solve for the unknown variable.

Answer 1

The Correct Option is B

Let the number to be added be \( x \).
The new numbers are: \[ 8 + x, \quad 21 + x, \quad 13 + x, \quad 31 + x \] The required condition: \[ \frac{8 + x}{21 + x} = \frac{13 + x}{31 + x} \] Cross multiplying: \[ (8 + x)(31 + x) = (13 + x)(21 + x) \] Expanding: \[ 248 + 8x + 31x + x^2 = 273 + 13x + 21x + x^2 \] \[ 248 + 39x = 273 + 34x \] \[ 39x - 34x = 273 - 248 \] \[ 5x = 25 \] \[ x = 5 \] Thus, the correct number to be added is 5.