If the numerator of a fraction is increased by 2
and denominator is decreased by 1, it
becomes. If the numerator is increased by 1
and denominator is increased by 2, it becomes
Find the fraction.
3
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Fraction\:is\: \frac{8}{15} \\ \\
Solution:
Let the fraction is
\frac{x}{y} \\ \\
according to the question,
\frac{x + 2}{y + 1} = \frac{5}{8} \\ \\ \\ 8(x + 2) = 5(y + 1) \\ \\ 8x + 16 = 5y + 5 \\ \\ 8x - 5y = - 11....eq1 \\ \\
now another statement is
\frac{x - 1}{y - 1} = \frac{1}{2} \\ \\ 2(x - 1) = y - 1 \\ \\ 2x - 2 - y = - 1 \\ \\ 2x - y = 1....eq2 \\ \\
Now solve equations 1 and 2
multiply eq2 by 4
8x - 5y = - 11 \\ 8x - 4y = 4 \\ - \: \: \: + \: \: \: \: \: \: - \\ - - - - - \\ - y = - 15 \\ \\ y = 15 \\ \\
put the value of y in eq2
2x - y = 1 \\ \\ 2x - 15 = 1 \\ \\ 2x = 16 \\ \\ x = 8 \\ \\
So the fraction is
\frac{8}{15} \\ \\
Hope it helps you.
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