Arithmetic

Ratio, Proportion & Variation

Medium

Two numbers are in the ratio of 3:5. If 9 is subtracted from each, the ratio becomes 12:23. Find the greater number.

✅ Correct Option: 1

The two numbers are in the ratio 3:5.

Let the first number $= 3x$ and the second number $= 5x$ for some common multiplier $x$ .

When 9 is subtracted from each number, the new ratio becomes 12:23.

$\frac{3x - 9}{5x - 9} = \frac{12}{23}$

$23(3x - 9) = 12(5x - 9)$

$69x - 207 = 60x - 108$

$69x - 60x = 207 - 108$

$9x = 99$

$x = 11$

The two numbers are:

First number $= 3x = 3 \times 11 = 33$

Second number $= 5x = 5 \times 11 = 55$

Therefore, the greater number is 55.

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Two numbers are in the ratio of 3:5. If 9 is subtracted from each, the ratio becomes 12:23. Find the greater number.

Solution

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