Question

The sum of two number is 100. If the fifth part of one is two more than the fourth part of the other, then find both the numbers.

Answer 1

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$let \: the \: number \: be \: = x \\ \frac{1}{5} x + \frac{1}{4}x + 2 = 100 \\ \frac{4x + 5x}{20} + 2 = 100 \\ \frac{9}{20}x + 2 = 100 \\ \frac{9}{20}x = 100 - 2 \\ \frac{9}{20}x = 98 \\ x = 98 \times \frac{20}{9} \\ x = \frac{1960}{9}$
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