Two numbers are such that if $7$ is added to the smaller number, then the sum is twice the greater and if $4$ is added to the greater number, then the sum is thrice the smaller number. Find the two numbers.

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Solution

Let two numbers are $x$ and $y,$ where $x > y$
$y + 7 = 2 x$
or $2 x - y = 7$ ......(i)
also $x + 4 = 3 y$
or $x - 3 y = - 4$ .....(ii)
Multiplying equation (ii) by $2$
$2 x - 6 y = - 8$
and then subtracting from (i), we get
$5 y = 15$
$\Rightarrow y = 3$
Now substituting the value of $y$ in (i), we get
$2 x - 3 = 7$
or $2 x = 10$
or $x = 5$
Hence, required numbers are $5$ and $3.$

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Two numbers are such that if 7 is added to the smaller number, then the sum is twice the greater and if 4 is added to the greater number, then the sum is thrice the smaller number. Find the two numbers.

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