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In a family of four members, the average age of the first three members is twice that of the fourth member. The average of the four members is 35 years. If the age of the fourth member is less than from only 2 members in the family, then what is the possible age of the youngest member?

In a family of four members, the average age of the first three members is twice that of the fourth member. The average of the four members is 35 years. If the age of the fourth member is less than from only 2 members in the family, then what is the possible age of the youngest member? Correct Answer 19

Given:

The average age of four members = 35 years

The average age of the first three members = 2 × age of the fourth member

The fourth member is less than from only 2 members in the family.

Concept:

Often the average refers to the arithmetic mean, the sum of the numbers divided by how many numbers are being averaged.

Formula used:

Average age = sum of all members age/total number of members

Calculation:

Let the age of the fourth member be x.

We know that the average age of the first three members is twice that of the fourth member

Then, sum of the age of the first three members = 2x × 3 = 6x

So the sum of the age of four members

⇒ 6x + x = 7x      ----(i)

But by question

The average of the four members is 35 years, then

Sum of the age of four members = 35 × 4 = 140 years      ----(ii)

Now we compare both equations

⇒ 7x = 140

⇒ x = 20 years

By question, the age of the fourth member is less than from only 2 members in the family

So the possible age of the youngest member is ≤ 20 years

∴ The possible age of the youngest member is 19 years

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