Question

The sum of two numbers is 110 . One fifth of the larger number is 8 more than one ninths of the smaller number. Find the numbers.

Answer 1

Solution:-
Let the first smaller number be 'x' and the larger number be 110 - x
So, according to the question.
$\frac{110-x}{5}-8=\frac{x}{9}$
Taking L.C.M. and solving it, we get.
$\frac{110-x-40}{5}=\frac{x}{9}$
Now, cross multiplying these, we get.
990 - 9x - 360 = 5x
630 = 5x + 9x
630 = 14x
x = $\frac{630}{14}$
x = 45
$\therefore$ Smaller number is 45 and the larger number is 110 - 45 = 65