Problems On Ages Practice Quiz - Exercise
1. The ratio of the ages of the father and the son at present is 7:1. After 4 years, the ratio will become 4 : 1. What is the sum of the present ages of the father and the son ?
A. 29 years
B. 35 years
C. 32 years
D. None of these
Answer - Option C
Explanation -
Father : Son = x : y = 7 : 1
After t = 4 year = α :β = 4 : 1
Son’s age = [latex]\frac{y * t(α - β) }{difference of cross product}[/latex]
[latex]\frac{1 * 4(4 - 1)}{7 * 1 - 4 * 1}[/latex]
[latex]\frac{1 * 4* 3}{3}[/latex] = 4 years
and Father’s age = [latex]\frac{x * t(α - β) }{difference of cross product}[/latex]
[latex]\frac{7 * 4(4 - 1)}{7 * 1 - 4 * 1}[/latex]
[latex]\frac{7 * 4* 3}{3}[/latex] = 28 years
Hence sum of the ages of father and son
= (28 + 4) = 32 years
2. If 10 years are subtracted from the present age of Ram and the remainder divided by 14, then you would get the present age of his grandson Shyam. If Shyam is 9 years younger to Sunder whose age is 14, then what is the present age of Ram?
A. 80 years
B. 70 years
C. 60 years
D. None of these
Answer - Option A
Explanation -
Let the Ram’s present age be x years, and Shyam’s present age be y years.
Now according to question
[latex]\frac{x - 10}{14}[/latex] = y
Now, Shyam is 9 years younger to sunder whose age
i.e, Present age of Shyam (y) = 14 – 9 = 5 years.
Putting the value of y in equations (1) will get [latex]\frac{x - 10}{14}[/latex] = 5
x = 80 years
3. A’s age is [latex]\frac{1}{6}[/latex]1 of B’s age. B’s age will be twice of C’s age after 10 years. If C’s eighth birthday was celebrated two years ago, then the present age of A must be
A. 5 years
B. 10 years
C. 15 years
D. 20 years
Answer - Option A
Explanation -
| A |
B |
C |
| 10 |
60 |
20 |
| 5x |
30x |
10x |
| 1x |
6x |
2x |
Now C’s eight birth day is celebrated two years ago is present age of
C = 10 years = 2x
i.e, x = 5
i.e, Present age of A = 1 * x = 1 * 5 = 5 years
4. Suresh is half his father’s age. After 20 years, his father’s age will be one and a half times Suresh’s age. What is his father’s age now?
A. 40 years
B. 20 years
C. 26 years
D. 30 years
Answer - Option A
Explanation -
Let father’s present age be x and that of Suresh be y
i.e, y = [latex]\frac{1x}{2}[/latex]
and x + 20 = [latex]\frac{3}{2}[/latex](y + 20)
From (i) and (ii), we have
x + 20 = [latex]\frac{3}{2}(\frac{x}{2} + 20)[/latex]
4x + 80 = 3x + 120
x = 40.
5. If Dennis is[latex]\frac{1}{{3}^{rd}}[/latex] the age of his father Keith now, and was [latex]\frac{1}{{4}^{th}}[/latex] the age of his father 5 years ago, then how old will his father Keith be 5 years from now ?
A. 20 years
B. 45 years
C. 40 years
D. 50 years
Answer - Option D
Explanation -
Dennis = [latex]\frac{1}{3}[/latex] Keith
Dennis – 5 = [latex]\frac{1}{4}[/latex](Keith – 5)
[latex]\frac{1}{3}[/latex] Keith - 5 = [latex]\frac{1}{4}[/latex]Keith – [latex]\frac{5}{4}[/latex]
Keith = 45
Hence Keith is 50 year s old, 5 years from now.
6. The ages of the two persons differ by 20 years. If 5 years ago, the older one be 5 times as old as the younger one, then their present ages, in years, are
A. 25, 5
B. 30, 10
C. 35, 15
D. 50, 30
Answer - Option B
Explanation -
Let ages of two persons be x and y.
i.e, x – y = 20 ...(i) [x > y]
x – 5 = 5(y – 5)
x – 5y = – 20 ...(ii)
Solving equations (i) and (ii)
i.e, y = 10, x = 30
7. Rajan got married 8 years ago. His present age is [latex]\frac{6}{5}[/latex] times his age at the time of his marriage. Rajan’s sister was 10 years younger to him at the time of his marriage. The age of Rajan’s sister is
A. 32 years
B. 36 years
C. 38 years
D. 40 years
Answer - Option C
Explanation -
Let the age at the time of marriage be x.
Then
x + 8 = [latex]\frac{6x}{5}[/latex]
Solving, we get x = 40.
i.e, Age of his sister = 40 – 10 + 8 = 38
8. A father’s age is three times the sum of the ages of his two children, but 20 years hence his age will be equal to the sum of their ages. Then the father’s age is
A. 30 years
B. 40 years
C. 35 years
D. 45 years
Answer - Option A
Explanation -
Let the sum of ages of two children = x years,
Let the father’s age = y years
i.e, y = 3x ...(i)
20 years hence, y + 20 = x + 20 + 20 ...(ii)
Solving (i) and (ii), we get
y = 30 years.
9. Ratio of Ashok’s age to Pradeep’s age is 4 : 3. Ashok will be 26 years old after 6 years. How old is Pradeep now?
A. 18 years
B. 21 years
C. 15 years
D. 24 years
Answer - Option C
Explanation -
Ashok’s present age = 26 – 6 = 20 years
i.e, [latex]\frac{Ashok's age}{Pradeep's age}[/latex] = [latex]\frac{4}{3}[/latex]
Hence Pradeep’s age = 15 years
10. Sonu is 4 years younger than Manu while Dolly is four years younger than Sumit but[latex]\frac{1}{5}[/latex]times as old as Sonu. If Sumit is eight years old, how many times as old is Manu as Dolly?
A. 6
B. [latex]\frac{1}{2}[/latex]
C. 3
D. None of these
Answer - Option A
Explanation -
Age of Sonu + 4 years = Age of Monu
Age of Dolly+ 4 years = Age of Sumit
If Sumit is 8 year old, than Dolly is 4 year old and Sonu is 20 year old.
Monu = 24 year
then [latex]\frac{Monu}{Dolly}[/latex] = [latex]\frac{24}{4}[/latex] = 6
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