Question

The average age of 11 players of a cricket team is increased by 2 months, when two of them aged 20 years and 21 years, respectively, are replaced by two new players. Find the average age of the two new players (in years).

• A. 18 5/12
• B. 21 5/12
• C. 18 1/4
• D. 20 1/2

Answer 1

Answer:

B. 21 5/12

Average increases by 2 months when two players are replaced

Convert months to years

$2 months = ( \frac{2}{12} = \frac{1}{6} ) year$

Increase in total age of team

Number of players = 11

Increase in total age:

$11 \times \frac{1}{6} = \frac{11}{6} \text{ years}$
So, total age increased by ( $\frac{11}{6}$)years.

Age of removed players

Removed ages:

20 + 21 = 41 years

Let sum of ages of new players = X

Net increase:

$X - 41 = \frac{11}{6}$
$X = 41 + \frac{11}{6}$
$X = \frac{246 + 11}{6}$
$X = \frac{257}{6}$

Average age of two new players

$\text{Average} = \frac{\frac{257}{6}}{2}$
$= \frac{257}{12}$
$= 21 \frac{5}{12}$