Question:
If the sum of the ages of two people is 83 and the difference between their ages is 25, then find their ages.
Correct Answer
54 years and 29 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 = 83
And, the difference between their ages = 25
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 = 83
⇒ a + b = 83 - - - - (i)
And, the age of the 1st people – the age of the 2nd people = 25
⇒ a – b = 25 - - - - (ii)
Now, after adding equation (i) and equation (ii), we get
a + b = 83/a – b = 25/ 2a = 108
⇒ 2a = 108
⇒ a = 108/2
⇒ a = 54
Thus, the age of 1st people = 54 years
Now, after substituting the value of a in the equation (i), we get
The equation (i) is a + b = 83
⇒ 54 + b = 83
After transposing 54 to RHS
⇒ b = 83 – 54 = 29
Thus, the age of the 2nd people = 29 years
Thus, the ages of the given people are 54 years and 29 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 = 83
And, the difference between the ages of the given two people = 25
Step (1)
Add the given ages i.e. the sum and the difference of ages
The sum of the ages + Difference between the ages
= 83 + 25
= 108
Step (2)
Divide the result by 2
= 108/2 = 54
Thus the age of 1st people = 54
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
= 83 – 54 = 29
Thus, the age of 2nd people = 29
Thus, the ages of the given people are 54 years and 29 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 = 83
And, the difference between the ages of the given two people = 25
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
= 83 – 25
= 58
Step (2)
Divide the result by 2
= 58/2 = 29
Thus the age of one people = 29
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
= 83 – 29 = 54
Thus, the age of another people = 54
Thus, the ages of the given people are 29 years and 54 years
Or, the ages of the given people are 54 years and 29 years Answer
Similar Questions
(1) If the sum of the ages of two people is 56 and the difference between their ages is 16, then find their ages.
(2) If the sum of the ages of two people is 41 and the difference between their ages is 11, then find their ages.
(3) If the sum of the ages of two people is 63 and the difference between their ages is 5, then find their ages.
(4) If the sum of the ages of two people is 41 and the difference between their ages is 5, then find their ages.
(5) If the sum of the ages of two people is 107 and the difference between their ages is 33, then find their ages.
(6) If the sum of the ages of two people is 44 and the difference between their ages is 12, then find their ages.
(7) If the sum of the ages of two people is 43 and the difference between their ages is 11, then find their ages.
(8) If the sum of the ages of two people is 79 and the difference between their ages is 23, then find their ages.
(9) If the sum of the ages of two people is 52 and the difference between their ages is 14, then find their ages.
(10) If the sum of the ages of two people is 122 and the difference between their ages is 38, then find their ages.