Two numbers are in the ratio $5 : 7$ . If $3$ is subtracted from each of them, and the ratio becomes $2 : 3$ . Find the numbers.

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Solution

Let Two numbers be to $5 x$ and $7 x$ , $3$ is subtracted from each of them
$\frac{5 x - 3}{7 x - 3} = \frac{2}{3} 3 \times (5 x - 3) = 2 \times (7 x - 3) 15 x - 9 = 14 x - 6 15 x - 14 x = 9 - 6 x = 3$
$5 x = 5 \times 3 = 15 7 x = 7 \times 3 = 21$
$∴$ The two numbers are $15$ and $21$

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Two numbers are in the ratio 5:7. If 3 is subtracted from each of them, and the ratio becomes 2:3. Find the numbers.

Let Two numbers be to 5x and 7x, 3 is subtracted from each of them5x-37x-3=233×5x-3=2×(7x-3)15x-9=14x-615x-14x=9-6x=35x=5×3=157x=7×3=21∴The two numbers are 15 and 21

Two numbers are in the ratio $5 : 7$ . If $3$ is subtracted from each of them, and the ratio becomes $2 : 3$ . Find the numbers.

Let Two numbers be to $5 x$ and $7 x$ , $3$ is subtracted from each of them
$\frac{5 x - 3}{7 x - 3} = \frac{2}{3} 3 \times (5 x - 3) = 2 \times (7 x - 3) 15 x - 9 = 14 x - 6 15 x - 14 x = 9 - 6 x = 3$
$5 x = 5 \times 3 = 15 7 x = 7 \times 3 = 21$
$∴$ The two numbers are $15$ and $21$