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At present, the respective ratio between the ages of A and B is 3:4 and that between A and C is 1:2. six years hence, the sum of A, B and C will be 96 years. what is the present age of A?
- a)12 years
- b)24 years
- c)19 years
- d)27 years
- e)18 years
Correct answer is option 'E'. Can you explain this answer?
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Verified Answer
At present, the respective ratio between the ages of A and B is 3:4 an...
The ratio between A, B and C is = 3:4:6
The sum of present age of A,B and C = 96 – 18 = 78
13 x = 78
x = 6
Present age of A = 3x = 18
The sum of present age of A,B and C = 96 – 18 = 78
13 x = 78
x = 6
Present age of A = 3x = 18
Most Upvoted Answer
At present, the respective ratio between the ages of A and B is 3:4 an...
Given:
The ratio between the ages of A and B is 3:4.
The ratio between the ages of A and C is 1:2.
Six years hence, the sum of A, B, and C will be 96 years.
To find:
The present age of A.
Solution:
Let's assume the present ages of A, B, and C as 3x, 4x, and 2y respectively.
Ratio between A and B:
According to the given information, the ratio between the ages of A and B is 3:4.
So, (3x)/(4x) = 3/4.
Cross-multiplying, we get 12x = 12x.
This means the ratio is satisfied.
Ratio between A and C:
According to the given information, the ratio between the ages of A and C is 1:2.
So, (3x)/(2y) = 1/2.
Cross-multiplying, we get 6x = 2y.
Sum of A, B, and C after 6 years:
After 6 years, the ages of A, B, and C will be (3x + 6), (4x + 6), and (2y + 6) respectively.
According to the given information, the sum of A, B, and C after 6 years will be 96.
So, (3x + 6) + (4x + 6) + (2y + 6) = 96.
Combining like terms, we get 7x + 2y + 18 = 96.
Simplifying the equation, we have 7x + 2y = 78.
Solving the equations:
Now, we have two equations:
1. 6x = 2y (from the ratio between A and C)
2. 7x + 2y = 78 (from the sum of A, B, and C after 6 years)
Multiplying equation 1 by 3, we get 18x = 6y.
Substituting this value in equation 2, we have 7x + (18x/3) = 78.
Simplifying the equation, we get 7x + 6x = 78.
Combining like terms, we have 13x = 78.
Dividing both sides of the equation by 13, we get x = 6.
Present age of A:
The present age of A is 3x.
Substituting the value of x, we have A = 3 * 6 = 18 years.
Therefore, the present age of A is 18 years (Option E).
The ratio between the ages of A and B is 3:4.
The ratio between the ages of A and C is 1:2.
Six years hence, the sum of A, B, and C will be 96 years.
To find:
The present age of A.
Solution:
Let's assume the present ages of A, B, and C as 3x, 4x, and 2y respectively.
Ratio between A and B:
According to the given information, the ratio between the ages of A and B is 3:4.
So, (3x)/(4x) = 3/4.
Cross-multiplying, we get 12x = 12x.
This means the ratio is satisfied.
Ratio between A and C:
According to the given information, the ratio between the ages of A and C is 1:2.
So, (3x)/(2y) = 1/2.
Cross-multiplying, we get 6x = 2y.
Sum of A, B, and C after 6 years:
After 6 years, the ages of A, B, and C will be (3x + 6), (4x + 6), and (2y + 6) respectively.
According to the given information, the sum of A, B, and C after 6 years will be 96.
So, (3x + 6) + (4x + 6) + (2y + 6) = 96.
Combining like terms, we get 7x + 2y + 18 = 96.
Simplifying the equation, we have 7x + 2y = 78.
Solving the equations:
Now, we have two equations:
1. 6x = 2y (from the ratio between A and C)
2. 7x + 2y = 78 (from the sum of A, B, and C after 6 years)
Multiplying equation 1 by 3, we get 18x = 6y.
Substituting this value in equation 2, we have 7x + (18x/3) = 78.
Simplifying the equation, we get 7x + 6x = 78.
Combining like terms, we have 13x = 78.
Dividing both sides of the equation by 13, we get x = 6.
Present age of A:
The present age of A is 3x.
Substituting the value of x, we have A = 3 * 6 = 18 years.
Therefore, the present age of A is 18 years (Option E).
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Solutions for At present, the respective ratio between the ages of A and B is 3:4 and that between A and C is 1:2. six years hence, the sum of A, B and C will be 96 years. what is the present age of A?a)12 yearsb)24 yearsc)19 yearsd)27 yearse)18 yearsCorrect answer is option 'E'. Can you explain this answer? in English & in Hindi are available as part of our courses for Quant.
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