Question

Two numbers are in the ratio 1:2 .When 4 is added to each, the ratio becomes 2:3.Find the numbers?

• A. 2,4
• B. 8,16
• C. 4,8
• D. 9,27

Answer 1

Answer:

C. 4,8

The numbers are 4 and 8.

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• Set up the variables: Let the two numbers be $x$ and $2x$.

• Form the equation: Add 4 to both numbers to get the new ratio:
  $\frac{x + 4}{2x + 4} = \frac{2}{3}$

• Cross-multiply:
  $3(x + 4) = 2(2x + 4)$
  $3x + 12 = 4x + 8$

• Solve for $x$:
  $12 - 8 = 4x - 3x$
  $x = 4$

• Find the numbers:

  • First number: $x = \mathbf{4}$

  • Second number: $2x = 2 \times 4 = \mathbf{8}$