Question : The two numbers are in the ratio of 5 : 3. If 9 is subtracted from each, then the new ratio is 9 : 5. What are the two numbers?
Option 1: 50 and 30
Option 2: 45 and 27
Option 3: 90 and 54
Option 4: 15 and 45
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Correct Answer: 90 and 54
Solution : Let the numbers be $5x$ and $3x$ According to the question, $\frac{5x–9}{3x–9} = \frac{9}{5}$ ⇒ $25x–45 = 27x–81$ ⇒ $36 = 2x$ ⇒ $x = \frac{36}{2}$ ⇒ $x = 18$ Thus, the numbers are $(5 × 18) = 90$ and $(3 × 18) = 54$ Hence, the correct answers are 90 and 54.
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Question : The ratio of two numbers is 5 : 9. If 6 is added to the greater number and 6 is subtracted from the smaller number, the greater number becomes 6 times the smaller number. What are the numbers?
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?
Question : The product of two positive numbers is 240. If the ratio of the two numbers is 3 : 5, then what is the sum of the two numbers?
Question : Directions: Which two numbers should be interchanged to make the given equation correct? 9 + 30 × 15 – 18 ÷ 6 = 274
Question : Two numbers are in the ratio of 3 : 5. If their HCF is 8, then find the numbers.
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