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# Problem on Ages – Aptitude test, questions, shortcuts

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 u can determine age of y by using the formula shown below.

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)

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)

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)

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,

(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)

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)

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

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)

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,

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

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)

Let present age of brother be x and sister’s age be 34 – x.

 Past Age (5 Yrs Ago) Present Age Future Age (After 6 Yrs) Brother (x – 5) x (x + 6) = ? Sister (34 – x) – 5 (30 – x)

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)

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)
(4x+5)=3 (x+5)
(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)

After further 5 years, father will be 2.5 times of daughter’s age.

Important Formulas

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