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?
Option 1: 15 and 17
Option 2: 10 and 18
Option 3: 25 and 45
Option 4: 20 and 36
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Correct Answer: 10 and 18
Solution : Given: 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. Let the greater number and the smaller number be 9$x$ and 5$x$ respectively. According to the question, $9x+6=6(5x-6)$ ⇒ $30x-9x=36+6$ ⇒ $x=\frac{42}{21}$ ⇒ $x=2$ So, the numbers are (5 × 2) = 10 and (9 × 2) = 18 Hence, the correct answer is 10 and 18.
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Question : The difference between the two numbers is 45% of their sum. The ratio of the larger number to the smaller number is:
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?
Question : A number is divided in the ratio 5 : 7. When 6 is added to each, the ratio changes to 7 : 9. Find the greater number.
Question : Directions: Which two numbers should be interchanged to make the given equation correct? 9 + 30 × 15 – 18 ÷ 6 = 274
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?
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