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The ratio of the age of a man and his wife is 4 : 3. After 4 years this ratio will be 9 : 7. If at the time of the marriage, the ratio was 5 : 3, then how many years ago they were married?
- a)12 yrs
- b)8 yrs
- c)10 yrs
- d)15 yrs
- e)None of these
Correct answer is option 'A'. Can you explain this answer?
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Verified Answer
The ratio of the age of a man and his wife is 4 : 3. After 4 years thi...
Lets present ages of a man and his wife is 3x and 4x years respectively
Most Upvoted Answer
The ratio of the age of a man and his wife is 4 : 3. After 4 years thi...
Ratio of age of Men and wife = 4 : 3
Let present age of Men = 4X
Present age of wife = 3X
4 year later ,
age of Men = 4X + 4
age of wife = 3X + 4
A/Q -
4X + 4 ÷ 3X + 4 = 9/7
=> 28X + 28 = 27x + 36
=> X = 8
age of Men = 32
age of wife = 24
Let they married P years ago,
A/Q- 32 - P ÷ 24 - P = 5/3
=> 96 - 3P = 120 - 5P
=> P = 12 year
option ( A )
Let present age of Men = 4X
Present age of wife = 3X
4 year later ,
age of Men = 4X + 4
age of wife = 3X + 4
A/Q -
4X + 4 ÷ 3X + 4 = 9/7
=> 28X + 28 = 27x + 36
=> X = 8
age of Men = 32
age of wife = 24
Let they married P years ago,
A/Q- 32 - P ÷ 24 - P = 5/3
=> 96 - 3P = 120 - 5P
=> P = 12 year
option ( A )
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Community Answer
The ratio of the age of a man and his wife is 4 : 3. After 4 years thi...
Given Information:
- Ratio of man's age to his wife's age = 4 : 3
- After 4 years, the ratio will be 9 : 7
- Ratio of their ages at the time of marriage = 5 : 3
Solution:
Step 1: Set up equations
Let the current ages of the man and his wife be 4x and 3x respectively.
After 4 years, their ages will be 4x + 4 and 3x + 4 respectively.
According to the given information:
(4x + 4) / (3x + 4) = 9 / 7
Also, at the time of marriage:
4x / 3x = 5 / 3
Step 2: Solve the equations
From the first equation:
(4x + 4) / (3x + 4) = 9 / 7
=> 7(4x + 4) = 9(3x + 4)
=> 28x + 28 = 27x + 36
=> x = 8
So, the current ages of the man and his wife are 32 and 24 respectively.
From the second equation:
4x / 3x = 5 / 3
=> 4(8) / 3(8) = 5 / 3
=> 32 / 24 = 5 / 3
Step 3: Calculate the years since marriage
Since the ratio of their ages at the time of marriage is 5 : 3, the difference in their ages is 2 units.
This difference of 2 units is equal to 8 years (32 - 24).
Therefore, they were married 8 years ago.
Therefore, the correct answer is option b) 8 yrs.
- Ratio of man's age to his wife's age = 4 : 3
- After 4 years, the ratio will be 9 : 7
- Ratio of their ages at the time of marriage = 5 : 3
Solution:
Step 1: Set up equations
Let the current ages of the man and his wife be 4x and 3x respectively.
After 4 years, their ages will be 4x + 4 and 3x + 4 respectively.
According to the given information:
(4x + 4) / (3x + 4) = 9 / 7
Also, at the time of marriage:
4x / 3x = 5 / 3
Step 2: Solve the equations
From the first equation:
(4x + 4) / (3x + 4) = 9 / 7
=> 7(4x + 4) = 9(3x + 4)
=> 28x + 28 = 27x + 36
=> x = 8
So, the current ages of the man and his wife are 32 and 24 respectively.
From the second equation:
4x / 3x = 5 / 3
=> 4(8) / 3(8) = 5 / 3
=> 32 / 24 = 5 / 3
Step 3: Calculate the years since marriage
Since the ratio of their ages at the time of marriage is 5 : 3, the difference in their ages is 2 units.
This difference of 2 units is equal to 8 years (32 - 24).
Therefore, they were married 8 years ago.
Therefore, the correct answer is option b) 8 yrs.
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