If Riya's age is four times the age of Siya and if Riya's age is 24 yrs , find the age difference between Riya and Siya ?
Answer: D
Let Siya's age = \(x\)
Then Riya's age = \(4x\)
But given Riya's age = 24
\(\Rightarrow 4x=24\)
\(\Rightarrow x=6\)
Hence Siya's age = 6 yrs
\(\Rightarrow\) The age difference = 24 - 6 = 18 yrs.
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The ages of A and B are in the ratio 6:5 and the sum of their ages is 44 years. What will be the ratio of their ages after 8 years?
Answer: A
Let the present age of A and B be 5 \(x\) and 6 \(x\) respectively.
Therefore, According to problem,
5 \(x\) + 6 \(x\) = 44
\(\Rightarrow \) \(11x=44\)
\(\Rightarrow \) \(x =4\)
Present ages of A and B are 20 and 24 respectively.
After 8 years,
Ages of A and B are (20+8) and (24+8)
A = 28 years and B=32 years
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When Ram was born, his father was 32 years older than his brother and his mother was 25 years older than his sister. If Ram's brother is 6 years older than Ram and his mother is 3 years younger than his father, how old was Ram's sister when Ram was born ?
Answer: C
Ram age when he was born = 0 years
His brother's age = 6 year
His father's age = brother age + 32years = 6+32 = 38
His mother's age = father's age - 3 = 35
So sister's age = 35-25 = 10years.
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If two times of the daughter’s age in years is included to the mother’s age, the total is 70 and if two times of the mother’s age is included to the daughter’s age, the total is 95. So the Mother’s age is,
Answer: C
Let daughter’s age = \(A\) and mother’s age = \(B\) years
Given: \(2A+B = 70\) and \(A+2B = 95\)
Solving B , we will get \(B=40\)
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The age of a person is thrice the total ages of his 2 daughters. 0.5 decades hence, his age will be twice of the total ages of his daughters. Then what is the father’s current age? [0.5 Decades = 5 Years]
Answer: C
Let, Total of current ages of the 2 daughters is \(A\) years.
Then, father’s current age = 3A years.
\((3A + 5) = 2 (A +10)\)
\(\Rightarrow\) \(3A + 5 = 2A + 20\)
\(\Rightarrow A = 15\)
Therefore, father’s current age = 45 years.
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"I am five times as old as you were, when I was as old as you are", said a man to his son. Find out their present ages, if the sum of their ages is 64 years ?
Answer: B
Let the present age of the man be '\(P\)' and son be '\(Q\)',
Given, \( P + Q = 64 \) or \(Q = (64 - P)\)
Now the man says "I am five times as old as you were, when I was as old as you are",
So, \(P = 5[B - (P - Q)]\)
We get \(6P=10Q\)
Substitute value for \(Q\)
\(6P = 10(64 - P),\)
Therefore, \(P\) = 40 and \(Q\) = 24
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Ten years ago, Kumar was thrice as old as Sailesh was but 10 years hence, he will be only twice as old. Find Kumar’s present age ?
Answer: B
Let Kumar’s present age be "\(x\)" years and Sailesh’s present age be "\(y\)" years.
Then, according to the first condition,
\(x - 10 = 3(y - 10) => x - 3y = - 20 ........(1)\)
Now, Kumar’s age after 10 years = \((x + 10)\) years.
Sailesh’s age after 10 years = \((y + 10)\) years.
\((x + 10) = 2 (y + 10) => x - 2y = 10 ......(2)\)
Solving (1) and (2),
we get \(x\) = 70 and \(y\) = 30
Kumar’s present age = 70 years and Sailesh’s present age = 30 years.
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0.1 decates ago, Vijaya was quadrice as old as her daughter Simran. 0.6 decades hence, Vijaya’s age will beat her daughter’s age by 0.9 decades. The proportion of the current ages of Vijaya and Simran is : [ 0.1 Decates =1 Year; quadrice = 4 times]
Answer: D
Let, Ages of Vijaya and Simran – 1 year ago was \(4A\) and \(A\) years respectively.
Then, \([(4A + 1) + 6] - [(A + 1) + 6] = 9\)
\(\Rightarrow3A = 9 \)
\(\Rightarrow A=3\)
Needed Ratio = \((4A + 1) : (A + 1) = 13 : 4\)
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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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Present ages of Sameer and Anand are in the ratio of 5 : 4 respectively. Three years hence, the ratio of their ages will become 11 : 9 respectively. What is Anand's present age in years?
Answer: A
Let the present ages of Sameer and Anand be \(5x\)years and \(4x\)years respectively.
then \(\frac{5x+3}{4x+3}= \frac{11}{9}\)
\(\Rightarrow\) \(9\left ( 5x+3 \right )=11\left ( 4x+3\right )\)
\(\Rightarrow\) \(45x+27=44x+23\)
\(\Rightarrow \) \(45x - 44x = 33 - 27\)
\(\Rightarrow \) \(x = 6.\)
\(\therefore \) Anand's present age \(= 4x = 24 years\)
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