Question

The ratio of two numbers is \( \frac{1}{2} \). If the ratio becomes \( \frac{5}{8} \) when 4 is added to both the numbers, find the bigger number.

• A. 6
• B. 10
• C. 12
• D. 24

Hint:

Let the numbers be k and 2k, since their ratio is 1:2, then use the second ratio condition to find k.

Answer 1

The Correct Option is C

Step 1: Set up the two numbers using the given ratio.
Let the two numbers be x and y, with \( \frac{x}{y} = \frac{1}{2} \), so \( y = 2x \).

Step 2: Write the second condition as an equation.
When 4 is added to both numbers, the new ratio is 5:8.
\[ \frac{x+4}{y+4} = \frac{5}{8} \]

Step 3: Substitute y = 2x and cross multiply.
\[ 8(x+4) = 5(2x+4) \]
\[ 8x + 32 = 10x + 20 \]

Step 4: Solve for x.
\[ 32 - 20 = 10x - 8x \]
\[ 12 = 2x \Rightarrow x = 6 \]

Step 5: Find y and pick the bigger number.
\( y = 2x = 12 \). Since \( 12 > 6 \), the bigger number is 12.

Final Answer:
The bigger number is 12. \[ \boxed{12} \]