Question:
If the sum of the ages of two people is 152 and the difference between their ages is 48, then find their ages.
Correct Answer
100 years and 52 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 = 152
And, the difference between their ages = 48
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 = 152
⇒ a + b = 152 - - - - (i)
And, the age of the 1st people – the age of the 2nd people = 48
⇒ a – b = 48 - - - - (ii)
Now, after adding equation (i) and equation (ii), we get
a + b = 152/a – b = 48/ 2a = 200
⇒ 2a = 200
⇒ a = 200/2
⇒ a = 100
Thus, the age of 1st people = 100 years
Now, after substituting the value of a in the equation (i), we get
The equation (i) is a + b = 152
⇒ 100 + b = 152
After transposing 100 to RHS
⇒ b = 152 – 100 = 52
Thus, the age of the 2nd people = 52 years
Thus, the ages of the given people are 100 years and 52 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 = 152
And, the difference between the ages of the given two people = 48
Step (1)
Add the given ages i.e. the sum and the difference of ages
The sum of the ages + Difference between the ages
= 152 + 48
= 200
Step (2)
Divide the result by 2
= 200/2 = 100
Thus the age of 1st people = 100
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
= 152 – 100 = 52
Thus, the age of 2nd people = 52
Thus, the ages of the given people are 100 years and 52 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 = 152
And, the difference between the ages of the given two people = 48
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
= 152 – 48
= 104
Step (2)
Divide the result by 2
= 104/2 = 52
Thus the age of one people = 52
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
= 152 – 52 = 100
Thus, the age of another people = 100
Thus, the ages of the given people are 52 years and 100 years
Or, the ages of the given people are 100 years and 52 years Answer
Similar Questions
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(2) If the sum of the ages of two people is 151 and the difference between their ages is 47, then find their ages.
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