1. What is John’s present age, if after 10 years his age will be 5 times his age 5 years back.
A. 6.2 years
B. 7.7 years
C. 8.7 years
D. 10 years
Answer: Option C
Explanation:
1) Let John’s present age be x
2) John’s age before 5 years = (x - 5)
3) John’s age after 10 years = (x + 10)
We are given that, John’s age after 10 years (x + 10) is 5 times his age 5 years back (x – 5)
Therefore,
(x + 10) = 5 (x – 5)
Solving the equation, we get
x + 10 = 5x – 25
4x = 35
x = 8.75 years
2. Rahul is 15 years elder than Rohan. If 5 years ago, Rahul was 3 times as old as Rohan, then find Rahul's present age.
A. 32.5 years
B. 27.5 years
C. 25 years
D. 24.9 years
Answer: Option B
Explanation:
1) Let age of Rohan be y
2) Rahul is 15 years elder than Rohan = (y + 15). So Rahul’s age 5 years ago = (y + 15 – 5)
3) Rohan’s age before 5 years = (y – 5)
5 years ago, Rahul is 3 times as old as Rohan
(y + 15 – 5) = 3 (y – 5)
(y + 10) = (3y – 15)
2y = 25
y = 12.5
Rohan’s age = 12.5 years
Rahul’s age = (y + 15) = (12.5 + 15) = 27.5 years
3. One year ago, ratio of Harry and Peter age’s was 5 : 6 respectively. After 4 years, this ratio becomes 6 : 7. How old is Peter?
A. 25 years
B. 26 years
C. 31 years
D. 35 years
Answer: Option C
Explanation:
Hint: If ages in the numerical are mentioned in ratio A : B, then A : B will be Ax and Bx.
We are given that age ratio of Harry : Pitter = 5 : 6
1) Harry’s age = 5x and Peter’s age = 6x
2) One year ago, their age was 5x and 6x. Hence at present, Harry’s age = 5x +1 and Peter’s age = 6x +1
3) After 4 years,
Harry’s age = (5x +1) + 4 = (5x + 5)
Peter’s age = (6x +1) + 4 = (6x + 5)
4) After 4 years, this ratio becomes 6 : 7. Therefore,
[latex]\frac{Harry’s Age}{6}[/latex] = [latex]\frac{Peter’s Age}{7}[/latex]
[latex]\frac{(5x + 5) }{(6x + 5)}[/latex] = [latex]\frac{6 }{7}[/latex]
7 (5x + 5) = 6 (6x + 5)
X = 5
Peter’s present age = (6x + 1) = (6 x 5 + 1) = 31 years
Harry’s present age = (5x + 1) = (5 x 5 + 1) = 26 years
4. The age of mother 10 years ago was 3 times the age of her son. After 10 years, the mother’s age will be twice that of his son. Find the ratio of their present ages.
A. 11 : 7
B. 9 : 5
C. 7 : 4
D. 7 : 3
Answer: Option D
Explanation:
We are given that, age of mother 10 years ago was 3 times the age of her son
So, let age of son be x and as mother’s age is 3 times the age of her son, let it be 3x, three years ago.
At present: Mother’s age will be (3x + 10) and son’s age will be (x + 10)
After 10 years: Mother’s age will be (3x + 10) +10 and son’s age will be (x + 10) + 10
Mother’s age is twice that of son
(3x + 10) +10 = 2 [(x + 10) + 10]
(3x + 20) = 2[x + 20]
Solving the equation, we get x = 20
We are asked to find the present ratio.
(3x + 10) : (x + 10) = 70 : 30 = 7 : 3
5. Sharad is 60 years old and Santosh is 80 years old. How many years ago was the ratio of their ages 4 : 6?
A. 10 years
B. 15 years
C. 20 years
D. 25 years
Answer: Option C
Explanation:
Here, we have to calculate: How many years ago the ratio of their ages was 4 : 6
Let us assume x years ago
At present: Sharad is 60 years and Santosh is 80 years
x years ago: Sharad’s age = (60 – x) and Santosh’s age = (80 – x)
Ratio of their ages x years ago was 4 : 6
[latex]\frac{(60 – x) }{(80 – x)}[/latex] = [latex]\frac{4 }{6}[/latex]
6(60 – x) = 4(80 – x)
360 – 6x = 320 – 4x
x = 20
Therefore, 20 years ago, the ratio of their ages was 4 : 6