Question

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 1

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