Question : Two numbers are, respectively, 25% and 30% less than a third number. What is the ratio of the first two numbers, in the order mentioned in the previous statement?
Option 1: 6 : 5
Option 2: 5 : 6
Option 3: 14 : 15
Option 4: 15 : 14
Correct Answer: 15 : 14
Solution :
Let the third number be 100$x$
The first number is 25% less than 100$x$ = 100$x ~–~ 25x = 75x$
The second number is 30% less than 100$x$ = 100$x~–~ 30x = 70x$
⇒ Required Ratio = $\frac{\text{First number}}{\text{Second number}}$ = $\frac{75x}{70x}$ = $\frac{15}{14}$
Hence, the correct answer is 15 : 14.
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