Finding the Two Numbers

Video Explanation

Question

Two numbers are in the ratio 5 : 6. If 8 is subtracted from each of the numbers, the ratio becomes 4 : 5. Find the numbers.

Solution

Step 1: Let the Variables

Let the numbers be \(5x\) and \(6x\)

Step 2: Form the Equation

After subtracting 8 from each number:

\[ \frac{5x – 8}{6x – 8} = \frac{4}{5} \]

Step 3: Cross Multiply

\[ 5(5x – 8) = 4(6x – 8) \]

\[ 25x – 40 = 24x – 32 \]

\[ 25x – 24x = -32 + 40 \]

\[ x = 8 \]

Step 4: Find the Numbers

First number: \[ 5x = 5(8) = 40 \]

Second number: \[ 6x = 6(8) = 48 \]

Conclusion

The two numbers are:

\[ \boxed{40 \text{ and } 48} \]

Final Answer (For Exam)

The required numbers are 40 and 48.