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The ratio between two numbers is $7: 9 .$ If each number is increased by 44 , then the ratio becomes $11: 13 .$ Find their difference.

(a) 33

(b) 11

(c) 22

(d) 44

Solution

Let the numbers are $7 x$ and $9 x$

$\therefore$ From the question,

$\frac{7 x+44}{9 x+44}=\frac{11}{13}$

$\Rightarrow \quad x=11$

$\therefore$ First number $=7 x$

$=7 \times 11$

$=77$

Second number $=9 x$

$=9 \times 11$

$=99$

$\therefore \quad$ Required difference

$=99-77=22$; Ans.

$\therefore$ Correct option is  (c)

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