- Prepare
- All Platforms
- Programming
- Aptitude
- Syllabus
- Interview Preparation
- Interview Exp.
- Off Campus
- Prime Video
- Prime Mock

- PrepInsta Prime
- OffCampus
- The Job Company
- Placement Stats
- Prime Video
- Prime Mock

^{0}Notifications Mark All Read

No New notification

- Login
- Get Prime

Quants Menu

- HCF and LCM
- Number System
- Number Decimals & Fractions
- Surds and Indices
- Divisibility
- Ages
- LCM
- HCF
- Inverse
- Speed Time and Distance
- Work and Time
- Boats and Streams
- Pipes and Cisterns
- Averages
- Allegations and Mixtures
- Ratio and Proportions
- Simple & Compound Interest
- Simple Interest
- Compound Interest
- Percentages
- Profit & Loss
- Successive Discount 1
- Successive Discount 2
- AP GP HP
- Arithmetic Progressions
- Geometric Progressions
- Harmonic Progressions
- Probability
- Permutation & Combination
- Combination
- Circular Permutation
- Geometry
- Heights and Distances
- Perimeter Area and Volume
- Coordinate Geometry
- Venn Diagrams
- Set Theory
- Algebra
- Linear Equations
- Quadratic Equations
- Logarithms
- Clocks
- Calendars
- Clocks and Calendars
- Finding remainder of large powers

# Formulas For Ages

**Formulas For Problem on Ages**

Here on this page you will get to know about the Formulas For Ages. These type of Formulas are widely used in the Problem on Ages questions and are beneficial for solving the question in exams Quickly and Efficiently.

**Important Formulas on Ages**

- If the present age is
*x*, then*n*times the age is.**nx** - If the present age is
*x*, then age*n*years later/hence =**x + n.** - If the present age is
*x*, then age*n*years ago =*x*–*n*. - The ages in a ratio
*a*:*b*will beand*ax*.*bx* - If the present age is x, then \frac{1}{n} \ of age is \frac{x}{n} \

**Important Concepts on Problems on Ages**

### Concept 1

x years ago the age of A was n1 times the age of B, and at present A’s age is n2 times that of B, then;

A’s current =\frac{\left ( n_{1} -1\right )n_{2}x}{n_{1}-n_{2}} years.

and, B’s current age = \frac{\left ( n_{1} -1\right )x}{(n_{1}-n_{2})}years.

### Concept 2

The present age of A is n1 times the present age of B. After x years, age of A becomes n2 times the age of B, then;

A’s current = \frac{\left ( n_{2} -1\right )n_{2}x}{(n_{1}-n_{2})} years.

and, B’s current age =\frac{\left ( n_{2} -1\right )x}{(n_{1}-n_{2})} years.

### Concept 3

t1 years ago, the age of A was X times the age of B and after t2 years age of A becomes Y times the age of B, then;

A’s present age =\frac{\left (x)(t_{1}+ t_{2}\right )( y – 1)}{(x-y)} + t_{1}years

And B’s present age = \frac{t_{2}(y – 1)+t_{1}(x – 1)}{x – y}years

### Concept 4

The sum of present ages of A and B is X years, t years after, the age of A becomes Y times the age of B, then;

A’s present age =\frac{xy + t(y-1)}{y +1}years

And B’s present age= \frac{x- t(y-1)}{y+1} years

### Concept 5

The ratio of the present ages of A and B is p: q and after t years, it becomes r: s, then;

A’s present age = \frac{pt(r-s)}{ps-qr} years.

And, B’s present age = \frac{qt(r-s)}{ps-qr} years

### Concept 6

The sum of present ages of A and B is X years, t years ago, the age of A was Y times the age of B, then;

Present age of A =\frac{xy + t(y-1)}{y+1}years

And, the present age of B = \frac{x + t(y-1)}{y+1}years

### Question and Answer

**Question 1: Saina Nehwal is 8 years older than her cousin. Her cousin is 24 years younger than his mother. If the ratio between the ages of Saina and her cousin’s mother is 7 : 11. What will be the age of Saina’s cousin after 3 years?**

**A. 21 years****B. 20 years****C. 26 years****D. 23 years**

Answer: 23 years

Let the age of Saina = x, her cousin’s age = x – 8, Cousin’s mother age = x – 8 + 24

Ratio between the ages of Saina and her cousin’s mother is 7 : 11

x : x + 16 = 7 : 11

11 × x = (x + 16) × 7

11x = 7x + 112

4x = 112

x = 28

Saina’s cousin age = 28 – 8 = 20

After 3 years Saina’s cousin age = 20 + 3 = 23 years

**Question 2 : Tiger’s present age is acquired, if we subtract 9 years from Arav’s present age and divide the remainder by 14. If Mohan’s age is 8 years and he is 3 years elder to Arav, then find Tiger’s present age.**

**A. 42****B. 79****C. 77****D. 85**

Answer : 79 years

Explanation:

Let Tiger’s present age be x

Given, Mohan’s present age 8 years

Then, Arav’s present age = 8-3 = 5 years

Given, if we subtract 9 years from Arav’s present age and divide the remainder by 14 we will get Tiger’s present age

= x-9/14 = 5

x-9 = 70

x = 79 years

Tiger’s present is 79 years

**Question 3 : ****Erika was five times older than Gigi ten years ago. The age of an Erika will be twice that of a Gigi in five years. How old were Erika’s compared to Gigi five years ago?**

**A. 5:1****B. 3:1****C. 2:1****D. 4:1**

Answer : 3:1

Explanation :

Erika was 5 times older than Gigi 10 years ago.

Let the age of Gigi 10 years ago be x years.

∴ The age of Erika 10 years ago = 5x years

5 years from now, Erika will be twice older than Gigi.

∴ We can write now,

(5x + 10 + 5) = 2 × (x + 10 + 5)

⇒ 5x + 15 = 2x + 30

⇒ 3x = 15

⇒ x = 5

∴ Age of Gigi 10 years ago = 5 years

And, the age of Erika 10 years ago = 5x = 5 × 5 = 25 years

∴ The reqd. ratio = \frac{25 + 5}{5+5} = \frac{30}{10} = 3:1

**Question 4 : Sum of the ages of Tendulkar and Dravid 16 years hence will be equal to 3 times their present age. If at present Tendulkar is 10 years elder to Dravid, then what are their present ages?**

**A. 22, 8****B. 29, 12****C. 13, 3****D. 13, 6**

Answer: 13, 3

Let the present ages of Tendulkar and Dravid be x years and y years respectively.

As per the question,

(x + 16) + (y + 16) = 3(x + y)

x + y + 32 = 3x + 3y

x + y = 16 …..(i)

Also,

y + 10 = x

x – y = 10 …..(ii)

Solving eqns (i) and (ii), we get

x = 13 and y = 3

Therefore, Present ages of Tendulkar and Dravid is 13 years and 3 years respectively.

**Question 5 : Amitabh said to his friend “If you subtract 18 from my age the two digits of my age will reverse their positions. Also my age is six, less than 8 times the sum of digits of my age”. Find Amitabh’s age.**

**A. 46 years****B. 37 years****C. 56 years****D. 42 years**

Answer:

Let Mayank’s age be (10x + y) years

Age by reversing the digits = (10y + x) yrs

Now, 10x + y − 18= 10y + x

9x – 9y = 18

x – y = 2………………(1)

Also,

10x+y = 8(x+y) – 6

2x – 7y = –6……….… (2)

Solving equations (1) and (2),

x = 4 , y = 2

Therefore, Mayank’s age = 10x + y

= 10(4) + 2

= 42 years

### Related Banners

Get PrepInsta Prime & get Access to all 200+ courses offered by PrepInsta in One Subscription

## Also Check Out

**Get over 200+ course One Subscription**

Courses like AI/ML, Cloud Computing, Ethical Hacking, C, C++, Java, Python, DSA (All Languages), Competitive Coding (All Languages), TCS, Infosys, Wipro, Amazon, DBMS, SQL and others

- HCF and LCM – Questions Formulas | How to Solve Quickly | Tricks & Shortcuts
- Number System – Questions | Formulas | How to Solve Quickly | Tricks & Shortcuts
- Number Decimals & Fractions – Questions | Formulas | How to Solve Quickly | Tricks & Shortcuts
- Surds and Indices – Questions | Formulas | How to Solve Quickly | Tricks & Shortcuts
- Divisibility – Questions | Formulas | How to Solve Quickly | Tricks & Shortcuts

- LCM – Questions | Formulas | How to Solve Quickly | Tricks & Shortcuts
- HCF – Questions | Formulas | How to Solve Quickly | Tricks & Shortcuts
- Inverse – Questions | Formulas | How to Solve Quickly | Tricks & Shortcuts

- HCF and LCM –

Questions

Formulas |

How to Solve Quickly |

Tricks & Shortcuts - Number System –

Questions |

Formulas |

How to Solve Quickly |

Tricks & Shortcuts - Number Decimals & Fractions –

Questions |

Formulas |

How to Solve Quickly |

Tricks & Shortcuts - Surds and Indices-

Questions |

Formulas |

How to Solve Quickly |

Tricks & Shortcuts - Divisibility –

Questions |

Formulas |

How to Solve Quickly |

Tricks & Shortcuts

Login/Signup to comment