Question

19. The ratio of two numbers is 5:9. If each number is decreased by 5, the ratio becomes 5:11. Find the
numbers.
a. 30, 19
b. 21, 37
C. 15, 34
d. 15, 27
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Answer 1

Hey mate here is the correct answer... .

see the attachment...

So the correct answer is option D

Thank you

Answer 2

let the numerator as x

let the denominator as y

so according to the question

$\frac{x}{y} = \frac{5}{9}$

or

$9x = 5y$

$x = \frac{5y}{9}$ (i)

according to the other equation

$\frac{x-5}{y-5} = \frac{5}{11}$

$11x - 55 = 5y - 25$

now putting the value of x from (I) in this equation

$11 \times \frac{5y}{9} - 55 = 5y - 25$

$\frac{55y}{9} - 55 = 5y - 25$

$\frac{55y}{9} - 5y = -25 + 55$

$\frac{55y - 45y}{9} = 30$

$10y = 270$

$y = \frac{270}{10} = 27$

supporting the value of y in (i)

$x = \frac{5 × 27}{9}$

$x = \frac{135}{9}$

$x = 15$

so the fraction is

$\frac{15}{27}$