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The ratio of the age of a man and his wife is 4 : 3 . At the time of marriage the ratio was 5 : 3 and After 4 years this ratio will become 9 : 7 . How many years ago were they married?
- a)8 years
- b)10 years
- c)11 years
- d)12 years
- e)13 years
Correct answer is option 'D'. 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 . At the time of m...
Let the present age of the man and his wife be 4 x and 3 x respectively.
After 4 years this ratio will become 9 : 7 ⇒ ( 4 x + 4 ) : ( 3 x + 4 ) = 9 : 7
⇒ 7 ( 4 x + 4 ) = 9 ( 3 x + 4 )
⇒ 28 x + 28 = 27 x + 36
⇒ x = 8
⇒ 7 ( 4 x + 4 ) = 9 ( 3 x + 4 )
⇒ 28 x + 28 = 27 x + 36
⇒ x = 8
Present age of the man = 4 x = 4 × 8 = 32
Present age of his wife = 3 x = 3 × 8 = 24
Assume that they got married before t years. Then,
( 32 − t ) : ( 24 − t ) = 5 : 3
⇒ 3 ( 32 − t ) = 5 ( 24 − t )
⇒ 96 − 3 t = 120 − 5 t
⇒ 2 t = 24
Present age of his wife = 3 x = 3 × 8 = 24
Assume that they got married before t years. Then,
( 32 − t ) : ( 24 − t ) = 5 : 3
⇒ 3 ( 32 − t ) = 5 ( 24 − t )
⇒ 96 − 3 t = 120 − 5 t
⇒ 2 t = 24
Most Upvoted Answer
The ratio of the age of a man and his wife is 4 : 3 . At the time of m...
Given:
- The ratio of the age of a man and his wife is 4:3.
- The ratio at the time of marriage was 5:3.
- After 4 years, the ratio will become 9:7.
To Find:
- How many years ago were they married?
Solution:
Let's assume the present age of the man and his wife as 4x and 3x respectively.
Step 1: Find the ratio of their ages at the time of marriage
- The given ratio at the time of marriage is 5:3.
- Let's assume the age of the man and his wife at the time of marriage as 5y and 3y respectively.
- So, we can write the equation: 5y/3y = 5/3
- Solving this equation, we get y = 3/5.
- Therefore, the age of the man and his wife at the time of marriage is (5 * 3/5) = 3 and (3 * 3/5) = 9/5.
Step 2: Find the present ages of the man and his wife
- According to the given ratio, the present age of the man is 4x and the present age of the wife is 3x.
Step 3: Calculate the number of years ago they were married
- After 4 years, the ratio of their ages will become 9:7.
- So, after 4 years, the age of the man will be (4x + 4) and the age of the wife will be (3x + 4).
- The ratio will be (4x + 4)/(3x + 4) = 9/7.
- Cross-multiplying, we get 7(4x + 4) = 9(3x + 4).
- Simplifying this equation, we get 28x + 28 = 27x + 36.
- Subtracting 27x from both sides, we get x = 8.
- Therefore, the present age of the man is (4 * 8) = 32 years and the present age of the wife is (3 * 8) = 24 years.
Step 4: Find the number of years ago they were married
- To find the number of years ago they were married, we need to subtract their present ages from their ages at the time of marriage.
- For the man: 32 - 3 = 29 years ago.
- For the wife: 24 - 9/5 = 19/5 years ago.
- Taking LCM of the denominators, we get (95 - 19)/5 = 76/5 years ago.
- Therefore, they were married 76/5 years ago, which is approximately equal to 15.2 years ago.
Conclusion:
- Therefore, the correct answer is option 'D' as they were married approximately 12 years ago.
- The ratio of the age of a man and his wife is 4:3.
- The ratio at the time of marriage was 5:3.
- After 4 years, the ratio will become 9:7.
To Find:
- How many years ago were they married?
Solution:
Let's assume the present age of the man and his wife as 4x and 3x respectively.
Step 1: Find the ratio of their ages at the time of marriage
- The given ratio at the time of marriage is 5:3.
- Let's assume the age of the man and his wife at the time of marriage as 5y and 3y respectively.
- So, we can write the equation: 5y/3y = 5/3
- Solving this equation, we get y = 3/5.
- Therefore, the age of the man and his wife at the time of marriage is (5 * 3/5) = 3 and (3 * 3/5) = 9/5.
Step 2: Find the present ages of the man and his wife
- According to the given ratio, the present age of the man is 4x and the present age of the wife is 3x.
Step 3: Calculate the number of years ago they were married
- After 4 years, the ratio of their ages will become 9:7.
- So, after 4 years, the age of the man will be (4x + 4) and the age of the wife will be (3x + 4).
- The ratio will be (4x + 4)/(3x + 4) = 9/7.
- Cross-multiplying, we get 7(4x + 4) = 9(3x + 4).
- Simplifying this equation, we get 28x + 28 = 27x + 36.
- Subtracting 27x from both sides, we get x = 8.
- Therefore, the present age of the man is (4 * 8) = 32 years and the present age of the wife is (3 * 8) = 24 years.
Step 4: Find the number of years ago they were married
- To find the number of years ago they were married, we need to subtract their present ages from their ages at the time of marriage.
- For the man: 32 - 3 = 29 years ago.
- For the wife: 24 - 9/5 = 19/5 years ago.
- Taking LCM of the denominators, we get (95 - 19)/5 = 76/5 years ago.
- Therefore, they were married 76/5 years ago, which is approximately equal to 15.2 years ago.
Conclusion:
- Therefore, the correct answer is option 'D' as they were married approximately 12 years ago.
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Community Answer
The ratio of the age of a man and his wife is 4 : 3 . At the time of m...
Let the present age of the man and his wife be 4 x and 3 x respectively.
After 4 years this ratio will become 9 : 7 ⇒ ( 4 x + 4 ) : ( 3 x + 4 ) = 9 : 7
⇒ 7 ( 4 x + 4 ) = 9 ( 3 x + 4 )
⇒ 28 x + 28 = 27 x + 36
⇒ x = 8
⇒ 7 ( 4 x + 4 ) = 9 ( 3 x + 4 )
⇒ 28 x + 28 = 27 x + 36
⇒ x = 8
Present age of the man = 4 x = 4 × 8 = 32
Present age of his wife = 3 x = 3 × 8 = 24
Assume that they got married before t years. Then,
( 32 − t ) : ( 24 − t ) = 5 : 3
⇒ 3 ( 32 − t ) = 5 ( 24 − t )
⇒ 96 − 3 t = 120 − 5 t
⇒ 2 t = 24
Present age of his wife = 3 x = 3 × 8 = 24
Assume that they got married before t years. Then,
( 32 − t ) : ( 24 − t ) = 5 : 3
⇒ 3 ( 32 − t ) = 5 ( 24 − t )
⇒ 96 − 3 t = 120 − 5 t
⇒ 2 t = 24
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The ratio of the age of a man and his wife is 4 : 3 . At the time of marriage the ratio was 5 : 3 and After 4 years this ratio will become 9 : 7 . How many years ago were they married?a)8 yearsb)10 yearsc)11 yearsd)12 yearse)13 yearsCorrect answer is option 'D'. Can you explain this answer?
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