Average - Study Mode

[#236] The average of prime numbers between 1 and 20 is-
Correct Answer

(B) $$9frac{5}{8}$$

Explanation

Solution: The prime number between 1 and 20 is 2, 3, 5, 7, 11, 13, 17, 19 ∴ Required average $$eqalign{
& = frac{{{ ext{sum of prime numbers}}}}{8} cr
& = frac{{2 + 3 + 5 + 7 + 11 + 13 + 17 + 19}}{8} cr
& = frac{{77}}{8} cr
& = 9frac{5}{8} cr} $$

[#237] Mr. Joe’s family consists of six people-himself, his wife and their four children. It is known that the average age of the family immediately after the birth of the first, second, third and fourth child was 16, 15, 16 and 15 years respectively. Find the age of Mr. Joe’s eldest son if the present average age of the entire family is 16 years -
Correct Answer

(B) 12 years

Explanation

Solution: When the first child was born, the total age of all the family members = (16 × 3) years = 48 years When the second child was born, the total age of all the family members = (15 × 4) years = 60 years By the time the second child was born, each one of the 3 family members had grown by $$eqalign{
& = left( {frac{{60 - 48}}{3}}
ight) cr
& = frac{{12}}{3} cr} $$ = 4 years Hence, the age of eldest son when the second child was born = 4 years When the third child was born, the total age of all the family members = (16 × 5) years = 80 years By the time, the third child was born, each one of the four family members had grown by = $$left( {frac{{80 - 60}}{4}}
ight)$$ = 5 years So, the age of the eldest son when the third child was born = (4 + 5) years = 9 years When the fourth child was born, the total age of all the family members = (15 × 6) years = 90 years By the time, the fourth child was born, each of the five family members had grown by = $$left( {frac{{90 - 80}}{5}}
ight)$$ = 2 years So, the age of the eldest son when the fourth child was born = (9 + 2) years = 11 years At present, the total age of all the 6 family members = (16 × 6) years = 96 years By now, each one of the 6 members have grown by = $$left( {frac{{96 - 90}}{6}}
ight)$$ xa0years = 1 year Hence, the present age of the eldest son = (11 + 1) years = 12 years

[#238] Out of 10 teachers of a school, on teacher retires and in place of him a new teacher 25 years old joins. As a result of it average age of the teachers reduces by 3 years. Age of the retired teacher ( in years) is :
Correct Answer

(A) 55

Explanation

Solution: Total number of teachers = 10 Age of new teacher = 25 years Age of the retire teacher = (25 + 3 × 10) years = 55 years

[#239] The average salary of all the workers in a workshop is Rs. 8000. The average salary of 7 technicians is Rs. 12000 and the average salary of the rest is Rs. 6000. The total number of workers in the workshop is-
Correct Answer

(B) 21

Explanation

Solution: Let the total number of workers be x. Then, ⇒ 8000x = (12000 × 7) + 6000(x - 7) ⇒ 2000x = 42000 ⇒ x = 21

[#240] The average age of a husband and his wife was 23 years at the times of their marriage. After five years they have a one-year old child. The average age of the family now is-
Correct Answer

(A) 19 years

Explanation

Solution: Sum of the present ages of husband, wife and child = (23 × 2 + 5 × 2) + 1 = 57 years ∴ Required average = $$left( {frac{{57}}{3}}
ight)$$ = 19 years