Two numbers are in the ratio 3:7. If 8 is added to both the numbers, their ratio becomes 5:9. The numbers are
12.28
To solve the problem, we need to first understand the formation of the ratios given in the question:
The original ratio of the two numbers is given as \(3:7\). Let's assume the numbers are \(3x\) and \(7x\) respectively.
According to the problem, if 8 is added to both the numbers, their ratio becomes \(5:9\).
This means:
\(\frac{3x + 8}{7x + 8} = \frac{5}{9}\)
Now, we solve this equation to find the value of \(x\):
Cross-multiplying gives us:
\(9(3x + 8) = 5(7x + 8)\)
Expanding both sides, we get:
\(27x + 72 = 35x + 40\)
Rearranging the terms to solve for \(x\):
\(72 - 40 = 35x - 27x\)
\(32 = 8x\)
\(x = 4\)
Now that we have the value of \(x\), we can find the original numbers:
\(3x = 3 \times 4 = 12\)
\(7x = 7 \times 4 = 28\)
Thus, the two numbers are 12 and 28.
Hence, the correct option is 12.28.
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