Average - Study Mode

[#161] The average age of a cricket team of 11 player is 27 year. If two more players are included in the team the average become 26 years. Then the average age (in year) of the two included player is:
Correct Answer

(B) 20.5

Explanation

Solution: Sum of the age of 11 player = 27 × 11 = 297 Sum of age of 11 player + 2 more included player = 13 × 26 = 338 ∴ Average of the included player $$ = frac{{338 - 297}}{2} = frac{{41}}{2} = 20.5$$

[#162] There is a group of 8 teachers. One teacher leaves the group and a new teacher joins the group. Due to this the average age of teachers becomes same as the average 2 years ago. If the member who left was aged 42 then what is the age (in years) of new teacher?
Correct Answer

(D) 26

Explanation

Solution: Old teacher age = 42 When one old teacher left the group and joins a new teacher, then average age of group become less 2 years. ∴ New teacher's age = [x08egin{array}{l}
x08egin{array}{*{20}{c}}
{42 - 8 imes 2}\
{,, downarrow }\
{{
m{total ,number ,of ,teachers}}}
end{array}\
= 42 - 16\
= 26{
m{ ,years}}
end{array}]

[#163] The average age of 10 children is 9 years 9 months. The average of 9 children is 8 years 11 months. What is the age of the tenth child ?
Correct Answer

(A) 17 years 3 months

Explanation

Solution: Average age of 10 children = 9 years 9 months Sum of ages of 10 children = 9 × 10 + $$frac{9}{12}$$ × 10 = $$frac{390}{4}$$ Average age of 9 children = 8 years 11 months Sum of age of 9 children = 8 × 9 + $$frac{11}{12}$$ × 9 = $$frac{321}{4}$$ Age of 10th child = $$frac{390}{4}$$ - $$frac{321}{4}$$ = $$frac{69}{4}$$ = 17 years 3 months

[#164] The average weight of 20 students in a class is increased by 0.75 kg when one student of 35 kg replaced by a new student. Weight of the new student (in kg) is :
Correct Answer

(D) 50

Explanation

Solution: Let the weight of the new student = x kg According to the question, $$frac{x - 35}{20}$$ = 0.75 ⇒ x - 35 = 15 ⇒ x = 50

[#165] In a pre school, the average weight of 30 girls in a class among 50 students is 16 kg and that of the remaining students is 15.5 kg. What is the average weight of all the students in the class ?
Correct Answer

(B) 15.8 kg

Explanation

Solution: According to the question, Average = $$frac{30 × 16 + 20 × 15.5}{50}$$ = $$frac{480 + 310}{50}$$ = $$frac{790}{50}$$ = 15.8 kg