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: Use one unknown instead of two.
Since the ratio of the numbers is 1:2, write the numbers directly as k and 2k for some number k, rather than naming them x and y separately.

Step 2: Add 4 to each and use the new ratio.
The new numbers are \( k+4 \) and \( 2k+4 \), and their ratio is 5:8.
\[ \frac{k+4}{2k+4} = \frac{5}{8} \]

Step 3: Cross multiply and simplify.
\[ 8(k+4) = 5(2k+4) \]
\[ 8k + 32 = 10k + 20 \]

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

Step 5: Write down both numbers.
The numbers are \( k = 6 \) and \( 2k = 12 \).

Final Answer:
The bigger number is 12, found here using a single unknown k instead of two separate variables. \[ \boxed{12} \]