Ten years ago, P was half of Q's age. If the ratio of their present ages is 3:4, what will be the total of their present age?
Answer: C
Let present age of P and Q be \(3x\) and \(4x\) respectively.
\(\left ( 3x-10 \right )=\frac{1}{2}\left ( 4x-10 \right )\)
\(\Rightarrow\) \(6x-20=4x-10\)
\(\Rightarrow\) \(2x=10\)
\(\Rightarrow \) \(x=5\)
Total of their present age is
\(=3x+4x=7x=7×5=35\)
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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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Father is aged three times more than his son. After 8 years, father would be two and a half times of son's age. After further 8 years, how many times would father be of son's age?
Answer: A
Assume that son's present age \(= x \)
Then, father's present age = \(3x+x=4x\)
After \(8\) years, father's age \(=2\tfrac{1}{2}\) times of son's age.
\(\Rightarrow\) \((4x+8)=2\tfrac{1}{2}(x+8)\)
\(\Rightarrow\) \(4x+8=\tfrac{5}{2}(x+8)\)
\(\Rightarrow\) \(8x+16=5x+40\)
\(\Rightarrow\) \(3x=40-16=24\)
\(\Rightarrow\) \(x=\frac{24}{3}=8\)
After further \(8\) years,
Son's age \( =x+8+8=8+8+8=24\)
Father's age \(=4x+8+8=4×8+8+8=48\)
Father's age/Son's age \(=\frac{48}{24}=2\)
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The sum of the ages of a father and son is \(45\) years. Five years ago, the product of their ages was four times the father's age at that time. The present age of father and son
Answer: C
Let son's age \(=x\) years.
Then father's age\(=(45-x)\) years.
\(\Rightarrow\) \((x-5)(45-x-5) = 4(45- x - 5)\)
\(\Rightarrow\) \((x-5)=4\)
\(\Rightarrow\) \(x=9\)
Their ages are \(36\) years and \(9\) 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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Rohit is younger than Rahul by 7 years. If the ratio of their ages is 7:9, find the age of Rohit
Answer: D
lets Rahul's age is \(x\) years
Then Rohit's age \(=(x-7)\) years
so, \(\frac{(x-7)}{x}=\frac{7}{9}\)
\(\Rightarrow \) \(9x-63=7x\)
\(\Rightarrow\) \(2x=63\)
\(\Rightarrow\) \(x=31.5\)
\(\therefore \) Rohit's age \(31.5-7=24.5\) years
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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 the man \(=(x+24)\) 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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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 sum of ages of 5 children born at the intervals of 3 years each is 50 years. What is the age of the youngest child?
Answer: A
Let the ages of children be \(x, (x + 3), (x + 6), (x + 9)\) and \((x+12)\) years
Then \(x + (x + 3) + (x + 6) + (x + 9) + (x + 12) = 50\)
\(\Rightarrow \) \(5x=20\)
\(\Rightarrow\) \(x=4\)
\(\therefore \) Age of the youngest child \(=x=4\) years
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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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