Question

Two number are in the ratio 3 : 5. If 9 is subtracted from each, the new numbers are in the ratio 12 : 23. The smaller number is:
A.27
B.33
C.49
D.55

Answer 1

I hope this would help you

Answer 2

$\huge\boxed{\texttt{\fcolorbox{Red}{aqua}{Hey Mate!!!}}}$
Let the number are 3x and 5x
If 9 is subtracted,
So The numbers are (3x - 9) and (5x - 9)
Now the numbers are in the ratio of 12 : 23
Hence
$\frac{3x - 9}{5x - 9} = \frac{12}{23} \\ 23(3x - 9) = 12(5x - 9) \\ 69x - 207 = 60x - 108 \\ 69x - 60x = 207 - 108 \\ 9x = 99 \\ x = \frac{99}{9} \\ x = 11 \\ so \: numbers \: are \\ 11 \times 3 = 33 \: \: and \\ 11 \times 5 = 55$
The smaller number is 33
Option B is your answer which is 33

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