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Two numbers are in ratio 1 : 2. If 4 is added to each the ratio becomes 2 : 3. The greater of the two numbers is
- a)4
- b)8
- c)16
- d)none of above
Correct answer is option 'B'. Can you explain this answer?
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Two numbers are in ratio 1 : 2. If 4 is added to each the ratio become...
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Two numbers are in ratio 1 : 2. If 4 is added to each the ratio become...
Given:
Two numbers are in the ratio 1:2.
Step 1: Setting up the equation
Let's assume the two numbers are x and 2x (since they are in the ratio 1:2).
When 4 is added to each number, the new ratio becomes 2:3. So, the new numbers will be x+4 and 2x+4.
Step 2: Writing the equation
According to the given information, we can set up the equation as follows:
(x+4)/(2x+4) = 2/3
Step 3: Solving the equation
To solve this equation, we can cross-multiply:
3(x+4) = 2(2x+4)
3x + 12 = 4x + 8
Now, we can solve for x:
12 - 8 = 4x - 3x
4 = x
Step 4: Finding the numbers
Now that we have found the value of x, we can substitute it back into our original assumption to find the numbers:
The smaller number = x = 4
The greater number = 2x = 2(4) = 8
Step 5: Verifying the ratio after adding 4 to each number
We need to verify that when 4 is added to each number, the ratio becomes 2:3.
The original ratio was 1:2, so we can check:
(4+4)/(8+4) = 8/12 = 2/3
Conclusion:
Therefore, the greater of the two numbers is 8 (option B) when the original numbers are in the ratio 1:2 and 4 is added to each number, resulting in a new ratio of 2:3.
Two numbers are in the ratio 1:2.
Step 1: Setting up the equation
Let's assume the two numbers are x and 2x (since they are in the ratio 1:2).
When 4 is added to each number, the new ratio becomes 2:3. So, the new numbers will be x+4 and 2x+4.
Step 2: Writing the equation
According to the given information, we can set up the equation as follows:
(x+4)/(2x+4) = 2/3
Step 3: Solving the equation
To solve this equation, we can cross-multiply:
3(x+4) = 2(2x+4)
3x + 12 = 4x + 8
Now, we can solve for x:
12 - 8 = 4x - 3x
4 = x
Step 4: Finding the numbers
Now that we have found the value of x, we can substitute it back into our original assumption to find the numbers:
The smaller number = x = 4
The greater number = 2x = 2(4) = 8
Step 5: Verifying the ratio after adding 4 to each number
We need to verify that when 4 is added to each number, the ratio becomes 2:3.
The original ratio was 1:2, so we can check:
(4+4)/(8+4) = 8/12 = 2/3
Conclusion:
Therefore, the greater of the two numbers is 8 (option B) when the original numbers are in the ratio 1:2 and 4 is added to each number, resulting in a new ratio of 2:3.
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Two numbers are in ratio 1 : 2. If 4 is added to each the ratio becomes 2 : 3. The greater of the two numbers isa)4b)8c)16d)none of aboveCorrect answer is option 'B'. Can you explain this answer?
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