Problems on Ages (Quick Tips and Tricks)
1) If the current age of a person be X, then
- age after n years = X + n
- age n years ago = X – n
- n times the age = nX
- If ages in the numerical are mentioned in ratio A : B, then A : B will be AX and BX
2) If sum of ages of x and y is A and ratio of their ages is p : q respectively, then one can determine age of y by using the formula :
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Age of y = (Ratio of y/sum of ratio) × sum of ages |
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Age of y =(q/(p + q))× A |
Points to Remember:
- After reading the question, assume unknown age by some variable x.
- Convert the statements in the question into mathematical equations.
- Calculate the unknown by solving the equations and the obtained value must satisfy the conditions given in the problem.
Numerical on ages can be generally classified into four types:
Type1: Calculate Present age
Q 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
Correct Option: (c)
Solution:
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
Q 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
Correct Option: (b)
Solution:
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
Type 2: Numerical to Determine Ages in ratio form
Q 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
Correct Option: (c)
Solution:
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,
Harry’s Age/6 = Peter’s Age/7
(5x + 5) / (6x + 5) = 6 / 7
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
Q 4. Age of mother 10 years ago was 3 times the age of her son. After 10 years, 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
Correct Option: (d)
Solution:
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
Type 3: Numerical to Determine Age of a Person before x Years
Q 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
Correct Option: (c)
Solution:
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
(60 – x)/(80 – x)=4/6
6(60 – x) = 4(80 – x)
360 – 6x = 320 – 4x
x = 20
Therefore, 20 years ago, the ratio of their ages was 4 : 6
Q 6. The ratio of Rohan’s age 4 years ago and Rahul’s age after 4 years is 1 : 1. If at present, the ratio of their ages is 5 : 3, then find the ratio between Rohan’s age 4 years hence and Rahul’s age 4 years ago.
a. 1 : 3
b. 3 : 1
c. 4 : 3
d. 3 : 4
Correct Option: (b)
Solution:
Hint: If ages in the numerical are mentioned in ratio A : B, then A : B will be Ax and Bx
1) At present: Ratio of their ages = 5 : 3.
Therefore, 5 : 3 will be 5x and 3x.
Rohan’s age 4 years ago = 5x – 4
Rahul’s age after 4 years = 3x + 4
2) Ratio of Rohan’s age 4 years ago and Rahul’s age after 4 years is 1 : 1
Therefore,
(5x – 4)/(3x + 4)=1/1
Solving, we get x = 4
3) We are asked to find the ratio between Rohan’s age 4 years hence and Rahul’s age 4 years ago.
Rohan’s age : (5x + 4)
Rahul’s age: (3x – 4)
Ratio of Rahul’s age and Rohan’s age
(5x + 4)/(3x – 4)=24/8=3/1
Type 4: Numericals to Determine Age of a Person after x Years
Q 7. 5 years ago, sister’s age was 5 times the age of her brother and the sum of present ages of sister and brother is 34 years. What will be the age of her brother after 6 years?
a. 12 years
b. 13.5 years
c. 15 years
d. 20 years
Correct Option : (c)
Solution:
We are given, 5 years ago sister’s age was 5 times the age of her brother.
Therefore,
(34 – x) – 5 = 5 (x – 5)
34 – x – 5 = 5x – 25
5x + x = 34 – 5 +25
6x = 54
x = 9
Future age (after 6 yrs) = (x + 6) = (9 + 6) = 15 years
Q 8. Father is 3 times more aged than his daughter. If after 5 years, he would be 3 times of daughter’s age, then further after 5 years, how many times he would be of his daughter’s age?
a. 1 (½) times
b. 2 times
c. 2.5 times
d. 3 times
Correct Option: (c)
Solution:
Let daughter’s age be x and father’s age be 3x.
Father’s age is 3 times more aged than his daughter, therefore father’s present age = x + 3x = 4x
After 5 years, father’s age is 3 times more than his daughter age.
(4x + 5) = 3 (x + 5)
x = 10
After 5 years it was (4x + 5), then after further 5 years, father’s age = (4x +10) and daughter’s age = (x + 10)
(4x + 10)/(x + 10)=?
Substitute the value of x, we get
[(4 × 10) + 10]/[10 + 10]=50/20=5/2=2.5
Free Mock Online Test for "Problems On Ages (Concepts & Related Solved Problems)":
https://gyangossip.com/problems-on-ages-part-1-/mock-test/T12809
https://gyangossip.com/problems-on-ages-part-2/mock-test/T12953
https://gyangossip.com/problems-on-ages-part-3-/mock-test/T13058