Question:
If the sum of the ages of two people is 122 and the difference between their ages is 38, then find their ages.
Correct Answer
80 years and 42 years
Solution And Explanation
Solution
Method (1) Algebraic Method to find the ages of the given people when the sum and the difference between ages are given.
Given, the sum of the age of two people = 122
And, the difference between their ages = 38
Then, find their ages = ?
Let the age of the 1st people = a
And, the age of the 2nd people = b
Now, according to question,
The age of the 1st people + The age of the 2nd people = 122
⇒ a + b = 122 - - - - (i)
And, the age of the 1st people – the age of the 2nd people = 38
⇒ a – b = 38 - - - - (ii)
Now, after adding equation (i) and equation (ii), we get
a + b = 122/a – b = 38/ 2a = 160
⇒ 2a = 160
⇒ a = 160/2
⇒ a = 80
Thus, the age of 1st people = 80 years
Now, after substituting the value of a in the equation (i), we get
The equation (i) is a + b = 122
⇒ 80 + b = 122
After transposing 80 to RHS
⇒ b = 122 – 80 = 42
Thus, the age of the 2nd people = 42 years
Thus, the ages of the given people are 80 years and 42 years Answer
Method (2) Shortcut Trick (1) to find the ages of the given people when the sum and the difference between ages are given.
As given in the question,
The sum of the ages of the two people = 122
And, the difference between the ages of the given two people = 38
Step (1)
Add the given ages i.e. the sum and the difference of ages
The sum of the ages + Difference between the ages
= 122 + 38
= 160
Step (2)
Divide the result by 2
= 160/2 = 80
Thus the age of 1st people = 80
Step (3)
Find the age of 2nd people by subtracting the age of 1st people from the sum of their ages as given in the question
Thus, the age of 2nd people = Sum of their ages – Age of 1st people
= 122 – 80 = 42
Thus, the age of 2nd people = 42
Thus, the ages of the given people are 80 years and 42 years Answer
Method (3) Shortcut Trick (2) to find the ages when sum and difference between ages of two people are given.
As given in the question,
The sum of the age of two people = 122
And, the difference between the ages of the given two people = 38
Step (1)
Subtract the given ages i.e. subtract the difference in ages from the sum of the ages
The sum of the ages – Difference in the ages
= 122 – 38
= 84
Step (2)
Divide the result by 2
= 84/2 = 42
Thus the age of one people = 42
Step (3)
Find the age of 2nd people by subtracting the calculated age of the one people from the sum of their ages as given in the question
Thus, the age of another people = Sum of their ages – Calculated age of one people
= 122 – 42 = 80
Thus, the age of another people = 80
Thus, the ages of the given people are 42 years and 80 years
Or, the ages of the given people are 80 years and 42 years Answer
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