The average age of six members of a family is 40 years. If the age of a guest is included, then the average age increases by 12.5%.What is the age (in years) of the guest?

Question

Question

This question was previously asked in

SSC CGL 2022 Tier-I Official Paper (Held On : 12 Dec 2022 Shift 4)

Answer 1

Given:

The average age of 6 members of a family is 40 years.

If the age of a guest is included, then the average age has increased by 12.5%.

Concept used:

Average = Sum of elements/number of elements

Calculation:

Sum of the age of 6 members of a family = 40 × 6

⇒ 240 years

If the age of a guest is included, then the average age has increased by 12.5%,

The average age of 7 persons = 40 × 112.5/100

⇒ 45 years

Sum of the age of 7 persons = 45 × 7

⇒ 315 years

Age of guest = 315 – 240

⇒ 75 years

∴ The age of the guest is 75.

Shortcut Trick

The average age of six members of a family is 40 years,

After the addition of 1 member, the average age increases by 12.5% the average age becomes = 40 × 9/8 = 45 year

The difference of average age is (45 - 40) = 5 year

So, the guest brings (5 × 7) = 35 year age extra

So, the age of the guest is (35 + 40) = 75 year