Age Equations

The section on quantitative aptitude includes Age Equation Problems. The questions in age equation problems are structured so that they result in equations. These equations will contain solutions that indicate the age of the people in the question, and they will be either linear or nonlinear.

Comparing two people’s ages at different times, such as now, in the past, or the future is a common theme in age word problems.

 Points to Note 

  • After reading the age issues, assume the unknown age is a variable, such as ‘X.’
  • Make mathematical equations out of the statements in the question.
  • Calculate the variable by solving the equations, and the resulting value must meet the problem’s requirements.

 Age calculations: How to Solve Them

Word problems can be perplexing since they include a lot of information, and we’re not always sure what to do with it. The procedure is as follows:

  1. Make a variable out of what we don’t know.
  2. Create an equation using the data you’ve been given.
  3. Find the unknown variable and solve for it.

4 Substitute our solution back into the equation to determine if the left and right sides of the equation are equal.

 Important age calculator formulas: 

  1. When the current age is x, n times the age = nx.
  2. When the current age is x, age n years later = x + n.
  3. When the current age is x, age n years ago = x – n.
  4. The ages in a ratio a: b  will be ax and bx.
  5. when the current age is x,1/n of the age is x/n

 What Is The Best Way for an Exact Age calculator?

If only one individual is involved, the problem is analogous to an Integer Problem. To figure out the relationship between the numbers, carefully read the problem. This is demonstrated in the single-person instances.

If 2 or more people are there in the age dilemma, employing a table is an excellent option. A table will assist you in organizing the data and writing the equations.

Example

Divya is two years older than Ronak, and their combined ages are 18. What are Ronak and Divya’s ages?

The first step in answering a word problem involving age is identifying the unknown and trying to express it as a variable, an alphabetical letter representing the unknown information. We don’t know Ronak’s or Divya’s ages in this problem. Because Ronak’s age is expressed as a percentage of Divya’s, our variable will be based on Divya’s age. In another way, let d be Divya’s age. Ronak’s age must be (d + 2) if he is two years older than Divya.

We can create our equation now that we have our variables. Because Ronak is two years older than Divya and their ages add up to 18, the calculation is:

d + d + 2 = 18

The next step is to solve the unknown variable, d, in the equation.

d + d + 2 = 18

2d + 2 = 18

2d = 16

d = 8

Therefore, Divya is 8 years old. We must substitute into Ronak’s equation to determine his age. Recall that Ronak’s age = d + 2. If d = 8, then Ronak’s age = 8 + 2 = 10.

The next is to verify that the left side of the equation equals the right side of the equation by putting our solution into the original equation.

d + d + 2 = 18

If d = 8, then:

8+8+2= 18

18=18

Therefore, the left and right sides are equal, Divya must be 8 years old, and Ronak must be 10 years old.

 Short tricks

  1. The total age of the brother and sister is 46. Seven years ago, the sum of their ages was four times the brother’s age. What is the recent age of the brother and sister?

Solution:

(B-7) (S-7) = 4(B-7)

S = 7 = 4

S = 11 years (present)

B=35 years (present)

 

  1. When two of the eight guys, aged 21 and 23, are replaced by two new men, the group’s average age rises by two years. What is the average of two new men?

Solution:

The numerator must be modified by 16 to modify the average age by 2 years. 2 years increase = 8 2 = 16

Two men = 21 + 23 = 44

 = 16 +44 = 60

Average 60/2 = 30 years

 Question for practice

  1.   Amy’s mother, Aashi, is 23 years her senior. Aashi will be twice Amy’s age in six years.?
  2.   Rahul is 4 years older than Mukesh. Their combined ages were 48 five years ago?
  3.   Shreya is four times Martha’s age. Their combined ages were 50 five years ago?
  4.   A vase is 22 years old, while a pitcher is 30 years old. How many years ago, the pitcher was twice as old as the vase?
  5.   Pankaj is two years younger than Rahul. Seven years ago, their ages added up to 13. What are their current ages?

 Conclusion

Age calculations are a useful tool for expressing conditions or relationships between two or more variables. There could be one, two, or three unknowns in an equation. The essential rule is that these equations are solvable if the number of unknowns equals the number of conditions; otherwise, they are not.