### Problems on Ages- Important Formulae, Tricks and Shortcuts [Quantitative Aptitude]

Here are important formulas and shortcuts to solve problems on ages. Basic knowledge regarding solving questions regarding problem on ages is important for various competitive exams like IBPS, SBI Bank PO, assistant, SSC exams, Railway exam, UPSC exams.

### Let the Present age of Lalit = Y years

Age of Deepak after 5 years = X + 5
Age of Deepak 6 yeas back = X - 6.
Age of Lalit 3 years hence = Y + 3
Age of Lalit 7 years age = Y - 7

To solve questions regarding problems on ages we have to make linear equation from the conditions given in the question. Below are some possible equations based on given conditions:

I. If Deepak is 7 years older than Lalit
• X = Y + 7

II. If Sum of ages of Deepak and Lalit is 45
• X + Y = 45

III. If Deepak is 4 times older than Lalit
• X = 4 * Y

IV. If 12 years back Deepak was thrice the age of Lalit
• (X - 12) = 3 * (Y - 12)

V. If ratio of ages of Deepak and Lalit is 2 : 3
• X/Y = 2/3 => X = 2Y/3

VI. If ratio of ages of Deepak and Lalit will be 3 : 4 after 4 years
• (X + 4) / (Y + 4) = 3 / 4

Example 1: Rahul's age after 10 years will be thrice than his age 10 years back. Find present age of Rahul?
Solution: Let present age of Rahul = X years
Rahul's age after 10 years = X + 10
Rahul's age before 10 years = X - 10 years
Given condition is : (X + 10) = 3 * (X - 10)
=> X = 20. Present age of Rahul

Example 2: Eighteen year age, a father was three times as old as his son. Now the father is only twice as old as his son. Then the sum of the present ages of the son and the father is-
Solution: Let the present age of father = X
Age of father 18 years age =  X - 18
Let the present age of son = Y
Age of son 18 years ago = Y - 18
From question: (X - 18) = 3 * (Y - 18) and X = 2Y
Solving above two equations : X = 36, Y = 72
So X + Y = 72 + 36 = 108.

Example 3: One year age ratio of Kunal's and Mohit's age was 6 : 7 respectively. Four years hence, this ratio would become 7 : 8. How old is Mohit?
Solution: Let the present age of Kunal = X
Age of Kunal one year ago = X - 1
Age of Kunal after 4 year = X + 4
Let the present age of Mohit = Y
Age of Mohit one year age = Y - 1
Age of Mohit after 4 years = Y + 4

One year ago: (X - 1)/(Y - 1) = 6/7 => 7X - 7 = 6Y - 6 => 7X - 6Y = 1
Four year hence: (X + 4)/(Y + 4) = 7/8 => 8X + 32 = 7Y + 28 => 8X - 7Y = - 4
Solving above equations: X = 31, Y = 36
Hence Mohit's present age is 36 years.

Example 4: If twice the age of Nikita is more than Ankit's age by 4 years and product of their present ages is 240. What will be the age of Nikita after 5 years?
Solution: Let Ankit's present age = X
Nikita's present age = Y
Now as given in question: 2 * Y = X + 4
and X * Y = 240 = > X = 240/Y
=>  2Y = 240/Y + 4 => 2Y2 - 4Y - 240 = 0
=> Y2 - 2Y - 120 = 0 =>  Y = 12, -10
So present age of Nikita is 12 years ( we will eliminate -10 as age can not be negative)
Nikita's age after 5 years = 12 + 5 = 17 years.

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