Average
- 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 years. The average age of new player is
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According to question ,
Average age of new players = 
(20 + 17) 11 × 2 
× 1 12 2 Average age of new players = 422 = 211 ⇒ 17 7 12 × 2 12 12
Correct Option: B
According to question ,
Average age of new players = (20 + 17) 11 × 2 × 1 12 2 Average age of new players = 422 = 211 ⇒ 17 7 12 × 2 12 12
∴ Average age of new players = 17 years 7 months
- The average age of 8 men is increased by 2 years when two of them whose age are 21 and 23 years replaced by two new men. The average age of the two new men is
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According to question ,
Overall increase in the total age = 8 × 2 = 16 years
∴ Total age of two new men = 21 + 23 + 16 = 60 years
∴ Average age of new men = 60 ÷ 2 = 30 years
Second method to solve this question with the help of given formula :
Here, X = 2, n = 8
Age of new person = Age of replaced person + XCorrect Option: D
According to question ,
Overall increase in the total age = 8 × 2 = 16 years
∴ Total age of two new men = 21 + 23 + 16 = 60 years
∴ Average age of new men = 60 ÷ 2 = 30 years
Second method to solve this question with the help of given formula :
Here, X = 2, n = 8
Age of new person = Age of replaced person + X
Age of new person = 24 + 2 × 8
Age of new person = 24 + 16 = 40 years
- The average age of four brothers is 12 years. If the age of their mother is also included, the average is increased by 5 years. The age of the mother (in years) is :
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Average age of 4 brothers = 12 yrs.
Total age of 4 brothers = 4 × 12 = 48 yrs.
Average age of 4 brothers + mother ( = 5 persons)
= 12 + 5 = 17 yrs.
∴ Total age of 4 brothers + mother = 5 × 17 = 85 yrs.
∴ The age of the mother = 85 – 48 = 37 yrs.
Second method to solve this question with the help of given formula :
Here, y = 5, n = 4
Age of mother = Average + y (n+1)Correct Option: A
Average age of 4 brothers = 12 yrs.
Total age of 4 brothers = 4 × 12 = 48 yrs.
Average age of 4 brothers + mother ( = 5 persons)
= 12 + 5 = 17 yrs.
∴ Total age of 4 brothers + mother = 5 × 17 = 85 yrs.
∴ The age of the mother = 85 – 48 = 37 yrs.
Second method to solve this question with the help of given formula :
Here, y = 5, n = 4
Age of mother = Average + y (n+1)
Age of mother = 12 + 5 (4 + 1)
Age of mother= 12 + 25 = 37 years
- The average of five numbers is 7. If three new numbers would be added, then the new average comes out to be 8.5. What is the average of those three new numbers?
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Here , The average of five numbers = 7
Sum of five numbers = 7 × 5
If three new numbers would be added, then
The average of 8 numbers = 8.5
Sum of 8 numbers = 8.5 × 8
Sum of three new numbers = 8 × 8.5 – 7 × 5 = 68 – 35 = 33Correct Option: C
Here , The average of five numbers = 7
Sum of five numbers = 7 × 5
If three new numbers would be added, then
The average of 8 numbers = 8.5
Sum of 8 numbers = 8.5 × 8
Sum of three new numbers = 8 × 8.5 – 7 × 5 = 68 – 35 = 33∴ Required average = 33 = 11 3
- A student finds the average of 10, two–digit numbers. If the digits of one of the numbers is interchanged, the average increases by 3.6. The difference between the digits of the 2-digit numbers is
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According to question,
Total increase = 3.6 × 10 = 36
∴ If the number be 10p + q, then
Number obtained after reversing the digits = 10q + p
∴ 10q + p – 10p – q = 36
⇒ 9q – 9p = 36Correct Option: A
According to question,
Total increase = 3.6 × 10 = 36
∴ If the number be 10p + q, then
Number obtained after reversing the digits = 10q + p
∴ 10q + p – 10p – q = 36
⇒ 9q – 9p = 36
⇒ 9 (q – p) = 36
⇒ q – p = 36 ÷ 9 = 4
