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The average age of eleven players of a cricket team decreases by 2 months when two new players are included in the team replacing two players of age 17 years and 20 yrs. The average age of new players is
- a)17 yrs 1 month
- b)17 yrs 7 month
- c)17 yrs 11 month
- d)18 yrs 3 month
Correct answer is option 'B'. Can you explain this answer?
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Given Information:
- Average age of eleven players decreases by 2 months when two new players are included in the team replacing two players of age 17 years and 20 years.
Let's solve step by step:
Step 1: Initial Average Age Calculation
- Let the initial average age of the team be A.
- The sum of ages of 11 players = 11A
- Given that two players of age 17 and 20 are replaced, their total age = 17 + 20 = 37.
- So, the initial total age of 11 players = 11A + 37.
Step 2: Final Average Age Calculation
- When two new players are included, the total age remains the same but the number of players increases to 11 + 2 = 13.
- Let the average age after including the new players be B.
- The sum of ages of 13 players = 13B.
- Given that the average age decreases by 2 months, we can write the equation:
11A - 2 = 13B
Step 3: Solving the Equations
- From Step 1 and Step 2:
11A + 37 = 13B
11A - 2 = 13B
- Solve these equations to find the initial average age A and final average age B.
Step 4: Calculating the Average Age of New Players
- Let the average age of new players be X.
- The sum of ages of the two new players = 2X.
- From Step 1 and Step 3:
(11A + 37) - 37 = 11X
11A = 11X
A = X
Therefore, the average age of the new players is the same as the initial average age of the team, which is 17 years 7 months. Hence, option B is correct.
- Average age of eleven players decreases by 2 months when two new players are included in the team replacing two players of age 17 years and 20 years.
Let's solve step by step:
Step 1: Initial Average Age Calculation
- Let the initial average age of the team be A.
- The sum of ages of 11 players = 11A
- Given that two players of age 17 and 20 are replaced, their total age = 17 + 20 = 37.
- So, the initial total age of 11 players = 11A + 37.
Step 2: Final Average Age Calculation
- When two new players are included, the total age remains the same but the number of players increases to 11 + 2 = 13.
- Let the average age after including the new players be B.
- The sum of ages of 13 players = 13B.
- Given that the average age decreases by 2 months, we can write the equation:
11A - 2 = 13B
Step 3: Solving the Equations
- From Step 1 and Step 2:
11A + 37 = 13B
11A - 2 = 13B
- Solve these equations to find the initial average age A and final average age B.
Step 4: Calculating the Average Age of New Players
- Let the average age of new players be X.
- The sum of ages of the two new players = 2X.
- From Step 1 and Step 3:
(11A + 37) - 37 = 11X
11A = 11X
A = X
Therefore, the average age of the new players is the same as the initial average age of the team, which is 17 years 7 months. Hence, option B is correct.
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The average age of eleven players of a cricket team decreases by 2 months when two new players are included in the team replacing two players of age 17 years and 20 yrs. The average age of new players isa)17 yrs 1 monthb)17 yrs 7 monthc)17 yrs 11 monthd)18 yrs 3 monthCorrect answer is option 'B'. Can you explain this answer?
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