Questions based on ages
Math MCQs

Question :    If the sum of the ages of two people is 134 and the difference between their ages is 42, then find their ages.

Correct Answer  88 years and 46 years

Solution & 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 = 134

And, the difference between their ages = 42

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 = 134

⇒ a + b = 134 - - - - (i)

And, the age of the 1st people – the age of the 2nd people = 42

⇒ a – b = 42 - - - - (ii)

Now, after adding equation (i) and equation (ii), we get

^{a + b  = 134/_{a – b  =   42}}/ _{2a       = 176}

⇒ 2a = 176

⇒ a = ¹⁷⁶/₂

⇒ a = 88

Thus, the age of 1st people = 88 years

Now, after substituting the value of a in the equation (i), we get

The equation (i) is a + b = 134

⇒ 88 + b = 134

After transposing 88 to RHS

⇒ b = 134 – 88 = 46

Thus, the age of the 2nd people = 46 years

Thus, the ages of the given people are 88 years and 46 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 = 134

And, the difference between the ages of the given two people = 42

Step (1)

Add the given ages i.e. the sum and the difference of ages

The sum of the ages + Difference between the ages

= 134 + 42

= 176

Step (2)

Divide the result by 2

= ¹⁷⁶/₂ = 88

Thus the age of 1st people = 88

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

= 134 – 88 = 46

Thus, the age of 2nd people = 46

Thus, the ages of the given people are 88 years and 46 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 = 134

And, the difference between the ages of the given two people = 42

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

= 134 – 42

= 92

Step (2)

Divide the result by 2

= ⁹²/₂ = 46

Thus the age of one people = 46

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

= 134 – 46 = 88

Thus, the age of another people = 88

Thus, the ages of the given people are 46 years and 88 years

Or, the ages of the given people are 88 years and 46 years Answer

Similar Questions

(1) If the sum of the ages of two people is 110 and the difference between their ages is 34, then find their ages.

(2) If the sum of the ages of two people is 88 and the difference between their ages is 26, then find their ages.

(3) If the sum of the ages of two people is 85 and the difference between their ages is 25, then find their ages.

(4) If the sum of the ages of two people is 25 and the difference between their ages is 5, then find their ages.

(5) If the sum of the ages of two people is 106 and the difference between their ages is 32, then find their ages.

(6) If the sum of the ages of two people is 145 and the difference between their ages is 45, then find their ages.

(7) If the sum of the ages of two people is 81 and the difference between their ages is 5, then find their ages.

(8) If the sum of the ages of two people is 55 and the difference between their ages is 5, then find their ages.

(9) If the sum of the ages of two people is 87 and the difference between their ages is 5, then find their ages.

(10) If the sum of the ages of two people is 31 and the difference between their ages is 5, then find their ages.