15. The numerator of a rational number is 5 less than its
denominator. If 2 is subtracted from the numerator and 2
is added to the denominator, the number becomes 2/5.
Find the rational number.
Answers
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Step-by-step explanation:
Let the denominator be x.
So, accordingly the numerator will be x-5.
A.T.Q:−
2 is added to denominator and subsequently subtracted from Numerator:-
\sf{\dfrac{(x-5)-2}{x+2}= \dfrac{2}{5}}x+2(x−5)−2=52
\sf{\dfrac{x-5-2}{x+2}= \dfrac{2}{5}}x+2x−5−2=52
\sf{\dfrac{x-7}{x+2}= \dfrac{2}{5}}x+2x−7=52
Cross multiplication:-
\sf{5(x-7)=2(x+2)}5(x−7)=2(x+2)
\sf{5x-35=2x+4}5x−35=2x+4
\sf{5x-2x = 4+35}5x−2x=4+35
\sf{3x = 39}3x=39
\sf{x = \dfrac{39}{3}}x=339
\sf{x = 13}x=13
The required Fraction is:-
\sf{\dfrac{13-5}{13}}1313−5
\sf{\purple{=\dfrac{8}{13}}}=138
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