Average - Study Mode
[#371] The average age of 24 boys and their teacher is 15 years. When the teacher's age is excluded, the average age decreases by 1 year. The age of the teacher is :
Correct Answer
(B) 39 years
Explanation
Solution: The total age of 24 boys and teacher is = 25 × 15 = 375 years Let the teacher's age = x years According to the question, 25 × 15 = 24 × 14 + x 375 = 336 + x x = 39 years
[#372] The average age of four boys A, B, C and D is 5 years and the average age A, B, D, E is 6 years. C is 8 years old. The age of E is (in years) :
Correct Answer
(A) 12
Explanation
Solution: According to the question, $$eqalign{
& frac{{A + B + C + D}}{4} = 5 cr
& A + B + C + D = 20.....(i) cr
& frac{{A + B + D + E}}{4} = 6 cr
& A + B + D + E = 24.....(ii) cr} $$ If C = 8 years old, put the value of 'C' in equation (i) ∴ A + B + D + 8 = 20 A + B + D = 12.....(iii) Put the value of equation (iii) in equation (ii) 12 + E = 24 E = 24 - 12 ∴ E = 12
[#373] A librarian purchased 50 storybooks for his library. But he saw that he could get 14 books more by spending Rs. 76 more but per book average becomes Rs. 1 less. The average price (in Rs.) of each book he bought, was :
Correct Answer
(D) 10
Explanation
Solution: Let the average price of 1 book = Rs. 1 According to the question, $$eqalign{
& Rightarrow frac{{50x + 76}}{{left( {50 + 14}
ight)}} = left( {x - 1}
ight) cr
& Rightarrow frac{{50x + 76}}{{64}} = x - 1 cr
& Rightarrow 50x + 76 = 64x - 64 cr
& Rightarrow 140 = 14x cr
& Rightarrow x = { ext{Rs}}{ ext{.}},10 cr} $$ Therefor average price of 1 book = Rs. 10
[#374] The average of odd numbers up to 100 is
Correct Answer
(C) 50
Explanation
Solution: Sum of odd numbers upto 100 = 1 + 3 + 5 +.....+ 99 = $$frac{50}{2}$$ [2 + (50 - 1) × 2] = 2500 [$$x08ecause $$ Sum of n terms of an A.P. with first term a and common difference] $$left[ {d = frac{n}{2}{ 2n + left( {n - 1}
ight)d} }
ight]$$ ∴ Required average = $$frac{2500}{50}$$ = 50
[#375] In a group of 120 people, one-fifth are men, one-fourth are women and the rest children. The average age of women is five-sixth of the average age of men. Average age of children is one-fourth of the average age of men. If average age of men is 60 years, what is the average age of the group?
Correct Answer
(A) 32.75 yeras
Explanation
Solution: Number of men = $$frac{1}{5}$$ × 120 = 24 Number of women = $$frac{1}{4}$$ × 120 = 30 Number of children = 120 - (24 + 30) = 66 Average age of men = 60 years Average age of children = $$frac{1}{4}$$ × 60 = 15 years Average age of women = $$frac{5}{6}$$ × 60 = 50 years ∴ Avarage age of the group $$eqalign{
& = left( {frac{{60 imes 24 + 50 imes 30 + 15 imes 66}}{{120}}}
ight){ ext{ years}} cr
& = left( {frac{{3930}}{{120}}}
ight){ ext{ years}} cr
& = 32.75{ ext{ years}} cr} $$