Question : Directions: The ratio of the ages of a man and his wife is 4 : 3. After 4 years, the ratio will be 9 : 7. If at the time of marriage, the ratio was 5 : 3, how many years ago were they married?
Option 1: 12
Option 2: 24
Option 3: 5
Option 4: 8
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Correct Answer: 12
Solution : The ratio of the present ages of a man and his wife = 4 : 3 So, the man's present age = 4a years, and his wife's present age = 3a years After four years, man's age = (4a + 4) years, and his wife's age = (3a + 4) years The ratio of the ages after 4 years = 9 : 7 Now, on comparing the ratio with the exact age value, ⇒ $\frac{4a + 4}{3a + 4} = \frac{9}{7}$ ⇒ 7(4a + 4) = 9(3a + 4) ⇒ 28a + 28 = 27a + 36 ⇒ 28a – 27a = 36 – 28 ⇒ a = 8 So, the man's present age = 32 years, and his wife's age = 24 years
Let they were married y years back. So, y years ago, the man's age = (32 – y) years, his wife's age = (24 – y) years From the question, ⇒ $\frac{32 – y}{24 – y} = \frac{5}{3}$ ⇒ 3(32 – y}) = 5(24 – y) ⇒ 96 – 3y = 120 – 5y ⇒ 5y – 3y = 120 – 96 ⇒ 2y = 24 ⇒ y = 12
So, they were married 12 years ago. Hence, the first option is correct.
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Question : Directions: 5 years hence, the ratio of ages of A and B will be 7 : 5 and the difference between their ages will be 4 years. What are the present ages (in years) of A and B respectively?
Option 1: 5, 9
Option 2: 6, 5
Option 3: 9, 5
Option 4: 9, 6
Question : Directions: The ratio of the present ages of P and Q is 5 : 8. Three years later their ages will be in the ratio 8 : 11. What is the present age (in years) of Q?
Option 1: 5
Option 2: 11
Option 3: 14
Question : Directions: A man was 32 years of age when he had his first son. His wife was 35 years of age when his son attained the age of 7 years. What is the difference between the age of the father and the mother?
Option 1: 7 years
Option 2: 3 years
Option 3: 5 years
Option 4: 4 years
Question : Eight years ago, the ratio of the ages of A and B was 5 : 4. The ratio of their present ages is 6 : 5. What will be the sum (in years) of the ages of A and B 7 years from now?
Option 1: 80
Option 2: 102
Option 3: 112
Option 4: 90
Question : The ratio of the present ages of Ram and Ramesh is 3 : 5. After 7 years the ratio of their ages will be 4 : 5. Find the present age of Ramesh.
Option 1: 5 years
Option 2: 15 years
Option 3: 7 years
Option 4: 12 years
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