A mother said her daughter , " I was as old as you are at present at the time of your birth. " If the mother age is 38 now, the daughter age 5 years back was ?
Answer: A
Let the son's present age be \(x\) years .
Then, \( (38 - x) = x \)
\(=> x= 19\)
Son's age 5 years back = (19-5) = 14 yeara
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When Raj Tarun was born, his father was 32 years older than his brother and his mother was 25 years older than his sister. If Raj Tarun's brother is 6 years older than Raj Tarun and his mother is 3 years younger than his father, how old was Raj Tarun's sister when Raj Tarun was born ?
Answer: B
Raj Tarun's age = 0 when he was born.
Then, given his brother is 6 years old.
Then his father is 6 + 32 = 38 when Raj Tarun was born
And his mother is 3 years yonger than his father => so his mother was 35 years old when Raj Tarun was born
and his sister is 25 year younger than his mother
so Raj Tarun's sister was 10 years old when Raj Tarun was born.
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The sum of the ages of 5 children born at the intervals of 3 years each is 50 years. What is the age of the youngest child ?
Answer: B
Let the age of the youngest child is '\(x \)' years.
Then the child elder than the yongest is '\(x + 3\)' yrs
Since each have 3yrs difference upto 5 children
And given that,
\(\Rightarrow x +x +3 + x+6 +x+9 + x+12 = 50\)
\(\Rightarrow 5x+30=50\)
\(\Rightarrow x= 4\) years.
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Ten years ago A was half of B in age. If the ratio of their present ages is 3 : 4, what will be the total of their present ages
Answer: C
Let A's age 10 years ago = \(x\) years
Then, B's age 10 years ago = \(2x\) years
\((x + 10) / (2x+ l0) = 3/4 \)
\(\Rightarrow x = 5.\)
So, the total of their present ages = \((x + 10 + 2x + 10) \)
\(= (3x + 20) = 35\) years
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The total age of A and B is 12 years more than the total age of B and C. C is how many year younger than A?
Answer: B
Write the condition algebraically.
\[ A + B = (B + C) + 12 \]
The \( B \) cancels from both sides:
\[ A - C = 12 \]
So C is 12 years younger than A. B's age never matters - which is why it is not given.
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A man is 24 years older than his son. In two years, his age will be twice the age of his son. The present age of his son is:
Answer: D
Let the son's present age be x years. Then, man's present age = \((x + 24) years.\)
\(\therefore (x + 24) + 2 = 2(x + 2)\)
\(\Rightarrow x + 26 = 2x + 4\)
\(\Rightarrow x = 22\)
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The age of father 10 years ago was thrice the age of his son. Ten years hence, father's age will be twice that of his son. The ratio of their present ages is:
Answer: B
Let the ages of father and son 10 years ago be \(3x\) and \(x\) years respectively
Then, \( (3x + 10) + 10 = 2[(x + 10) + 10]\)
\( \Rightarrow3x + 20 = 2x + 40\)
\(\Rightarrow x = 20.\)
\(\therefore\) Required ratio = \( (3x + 10) : (x + 10) = 70 : 30 = 7 : 3.\)
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Eight years ago, Ajay's age was 4/3 times that of Vijay. Eight years hence, Ajay's age will be 6/5 times that of Vijay. What is the present age of Ajay ?
Answer: B
Let the present ages of Ajay and Vijay be ' \(A\) ' and ' \(V\) ' years respectively.
\(\Rightarrow A-8= \frac{4}{3}\left ( V-8 \right )\) and \( A + 8 =\frac{6}{5}\left ( V-8 \right )\)
\(\Rightarrow\frac{3}{4}\left ( A-8 \right )= V-8\) and \(\frac{5}{6}\left ( A+8 \right )=V+8\)
\(V=\frac{3}{4}\left ( A-8 \right ) + 8=\frac{5}{6}\left ( A+8 \right )-8\)
\(\Rightarrow \frac{3}{4}A-6+8=\)\(\frac{5}{6}A + \frac{20}{3}- 8\)
\(\Rightarrow 10 -\frac{20}{3}=\)\(\frac{10}{12}A -\)\(\frac{9}{12}A\)
\(\Rightarrow \) \(\frac{10}{3}=\) \(\frac{A}{12}\)
\(\Rightarrow A = 40\)
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A person's present age is two-fifth of the age of his mother. After 8 years, he will be one-half of the age of his mother. How old is the mother at present ?
Answer: C
Let the mother's present age be \(x\) years.
Then, the person's present age = \(\frac{2}{5}x\)
\(\frac{2x}{5+8}x=\frac{1}{2}\left ( x+8 \right )\)
\(2(2x+40)=5\left ( x+8 \right )\)
\(x=40\)
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A man is 24 years older than his son. In two years, his age will be twice the age of his son. What is the present age of his son?
Answer: C
Let present age of the son \(=x\) years
Then, present age of the man is \((x+24)\) years
Given that, in 2 years, man's age will be twice the age of his son
\(\Rightarrow \) \((x+24)+2=2(x+2)\)
\(\Rightarrow \) \(x=22\)
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