Question : The difference between the two numbers is 45% of their sum. The ratio of the larger number to the smaller number is:
Option 1: 20 : 9
Option 2: 9 : 20
Option 3: 29 : 11
Option 4: 11 : 29
Correct Answer: 29 : 11
Solution :
Let the two numbers be $x$ and $y$.
According to the information given,
($x$ – $y$) = ($x$ + $y$) × $\frac{45}{100}$
⇒ 20$x$ – 20$y$ = 9$x$ + 9$y$
⇒ 11$x$ = 29$y$
$\therefore x$ : $y$ = 29 : 11
So, the ratio of the larger number to the smaller number is 29 : 11.
Hence, the correct answer is 29 : 11.
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