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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The sum of the present ages of a father and his son is 60 years. Six years ago, father's age was five times the age of the son. After 6 years, son's age will be:
Answer: D
Let the present ages of son and father be \(x\) and \((60-x)\) years respectively
Then , \((60-x)-6=5(x-6)\)
\( \Rightarrow \) \(54 - x=5x-30\)
\( \Rightarrow 6x=84\)
\( \Rightarrow x=14 \)
\( \therefore \) Son's age after 6 years = \(( x+ 6)\)= 20 years
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The ages of Krish and Vaibhav are in the proportion of 3 : 5. After 9 years, the proportion of their ages will be 3 : 4. Then the current age of Vaibhav is:
Answer: C
Let Krish's age be \(3A\) and Vaibhav's age be \(5A\)
\(\therefore(3A+9)/(5A+9) = 3/4\)
\(\Rightarrow 4 (3A + 9) = 3 (5A + 9) \)
\(\Rightarrow A=3\)
Therefore, Vaibhav’s age = 15 years.
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Rahul's age after 15 years will be 5 times his age 5 years back, What is the present age of Rahul?
Answer: B
Let Rahul's present age is \(x\) years.
Then \(x+15=5(x-5)\)
\(\Rightarrow\) \(4x=40\)
\(\Rightarrow\) \(x=10\)
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Ages of two persons differ by 16 years. If 6 year ago, the elder one be 3 times as old the younger one, find their present age
Answer: B
Let the age of younger person is \(x\)
Then elder person age is \((x+6)\)
so 6 years before
\(3(x-6) = (x+16-6)\)
\(\Rightarrow\) \((3x-18) =( x+10)\)
\(\Rightarrow\) \(x=14\)
So other person age is \(x + 16 = 30\)
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The ratio between the present ages of P and Q is 6:7. If Q is 4 years old than P, what will be the ratio of the ages of P and Q after 4 years
Answer: A
Let P age and Q age is \(6x\) years and \(7x\) years respectively
Then, \(7x-6x=4\)
\(\Rightarrow\) \(x=4\)
So required ratio will be \((6x+4): (7x+4)\)
\(\Rightarrow\) \(28:32\)
\(\Rightarrow 7:8\)
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A is three times as old as B. C was twice-as old as A four years ago. In four years' time, A will be 31. What are the present ages of B and C ?
Answer: C
Let the age of A = \(A\), B = \(B\) and C = \(C\)
From given,
\(A = 3B\)
4 years ago,
\(A + 4 = 31\)
\(\Rightarrow A=27\)
sub in above \(B\) , we get \(B\) = 9
\(C = 2(27 - 4) + 4 = 46 + 4 = 50 \)
Hence B = 9years and C = 50years.
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