Question : The ratio between the two numbers is 3 : 4. If each number is increased by 6, the ratio becomes 4 : 5. What is the difference of the numbers?
Option 1: 1
Option 2: 3
Option 3: 6
Option 4: 8
Correct Answer: 6
Solution : Given: The ratio between the two numbers is 3 : 4. If each number is increased by 6, the ratio becomes 4 : 5. Let the numbers be $3x$ and $4x$. As per given conditions, ⇒ $\frac{3x+6}{4x+6}=\frac{4}{5}$ ⇒ $15x+30=16x+24$ $\therefore x = 6$ $\therefore$ Required difference $=4x-3x=x=6$ Hence, the correct answer is 6.
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Question : The ratio of two numbers is 4 : 5. If both numbers are increased by 4 the ratio becomes 5 : 6. What is the sum of the two numbers?
Option 1: 9
Option 2: 18
Option 3: 27
Option 4: 36
Question : The ratio of two numbers is 3 : 5. If both numbers are increased by 8, the ratio becomes 13 : 19. What is the sum of the two numbers?
Option 1: 32
Option 2: 48
Option 3: 40
Option 4: 72
Question : The product of two numbers is 24 times the difference between these two numbers. If the sum of these numbers is 14, the larger number is:
Option 2: 8
Option 3: 7
Option 4: 10
Question : Two numbers are in the ratio 5 : 3 and the difference between these two numbers is 34. Find the smaller of the two numbers.
Option 1: 51
Option 2: 85
Option 3: 68
Option 4: 34
Question : The ratio of two numbers is 3 : 5. If eight is added to the first, and seven to the second, then the ratio becomes 2 : 3. What will the ratio become if six is added to each?
Option 1: 9 : 14
Option 2: 5 : 7
Option 3: 5 : 9
Option 4: 7 : 9
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