JIPMAT 2021 (QA) - In a cricket team of 11 players, the average age is 28 years. Out of these, the average ages of three groups of three players each are 25 years, 28 years, and 30 years respectively. If in these groups, the captain and the youngest player are not included and the captain is eleven years older than the youngest player, then the age of the captain is | PYQs + Solutions

JIPMAT 2021

Arithmetic

Averages

Conceptual

In a cricket team of 11 players, the average age is 28 years. Out of these, the average ages of three groups of three players each are 25 years, 28 years, and 30 years respectively. If in these groups, the captain and the youngest player are not included and the captain is eleven years older than the youngest player, then the age of the captain is

33 years

34 years

35 years

36 years

Correct Option: 3

Given:

\newline

- Players: 11

\newline

- Team average: 28 years

\newline

- Three groups of 3 players:

\frac{25+28+30}{3}

years

\newline

- Captain's age = Youngest player's age + 11

Let

x =

youngest player's age

Average of 9 players

= \frac{3×25 + 3×28 + 3×30}{9} = \frac{249}{9}

Using average formula:

\frac{9 × \frac{249}{9} + x + (x+11)}{11} = 28

\frac{249 + 2x + 11}{11} = 28

249 + 2x + 11 = 308

\newline

2x = 48

\newline

x = 24

Captain's age

= 24 + 11 = 35

years