The ratio of two numbers is 5:9. If ech number is decreased by 5, the ratio become 5:11.find the numbers.
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Answer:
let the numerator as x
let the denominator as y
so according to the question
\frac{x}{y} = \frac{5}{9}
y
x
=
9
5
or
9x = 5y9x=5y
x = \frac{5y}{9}x=
9
5y
(i)
according to the other equation
\frac{x-5}{y-5} = \frac{5}{11}
y−5
x−5
=
11
5
11x - 55 = 5y - 2511x−55=5y−25
now putting the value of x from (I) in this equation
11 \times \frac{5y}{9} - 55 = 5y - 2511×
9
5y
−55=5y−25
\frac{55y}{9} - 55 = 5y - 25
9
55y
−55=5y−25
\frac{55y}{9} - 5y = -25 + 55
9
55y
−5y=−25+55
\frac{55y - 45y}{9} = 30
9
55y−45y
=30
10y = 27010y=270
y = \frac{270}{10} = 27y=
10
270
=27
supporting the value of y in (i)
x = \frac{5 × 27}{9}x=
9
5×27
x = \frac{135}{9}x=
9
135
x = 15x=15
so the fraction is
\frac{15}{27}
27
15
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