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

Age of y = | Ratio of y | × sum of ages |

Sum of ratios |

Age of y = | q | × A |

(p + q) |

**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

View solution

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

View solution

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