Average - Study Mode

[#201] The average of all the odd integers between 2 an 22 is ?
Correct Answer

(B) 12

Explanation

Solution: Series → 3 + 5 + 7 . . . . . 21 Total numbers $$frac{{{ ext{Last term }} - { ext{ First term}}}}{{{ ext{Difference}}}}$$ xa0 xa0 + 1 = $$frac{21 - 3}{2}$$ + 1 = $$frac{18}{2}$$ + 1 = 10 Sum of series $$eqalign{
& = frac{n}{2}left[ {2a + left( {n - 1}
ight)d}
ight] cr
& = frac{{10}}{2}left[ {2 imes 3 + left( {10 - 1}
ight) imes 2}
ight] cr
& = 5left[ {6 + 9 imes 2}
ight] cr
& = 5 imes 24 cr
& = 120 cr} $$ Average = $$frac{120}{10}$$ = 12

[#202] The average weight of five persons sitting in a boat is 38 kg. The average weight of the boat and the persons sitting in the boat is 52 kg. What is the weight of the boat ?
Correct Answer

(B) 122 kg

Explanation

Solution: Let the five persons be A, B, C, D, E According to the question, = $$frac{A + B + C + D + E}{5}$$ xa0 xa0 = 38 kg = A + B + C + D + E = 190 kg.....(i) $$frac{{5,{ ext{persons}} + { ext{Boat}}}}{6} = 52$$ 5 persons + Boat = 312 kg.....(ii) ∴ Boat's weight = 312 - 190 = 122 kg

[#203] The average expenditure of a man for the first five months Rs. 1200 and for the next seven months is Rs. 1300. If he saves Rs. 2900 in that years, his monthly average income is -
Correct Answer

(D) Rs. 1500

Explanation

Solution: Total expenditure = 1200 × 5 + 1300 × 7 = Rs. 15100 Total savings = Rs. 2900 Total income = Rs. 18000 Average income = $$frac{18000}{12}$$ = 1500

[#204] The average age of mother and her six children is 12 years, which is reduced by 5 years if the age of mother is excluded. The age of the mother (in years) is :
Correct Answer

(C) 42

Explanation

Solution: Mother + 6 children = 12 × 7 = 84 years 6 children = 6 × 7 = 42 years ∴ Age of mother = 42 years

[#205] There are 50 students in a class. Their average weight is 45 kg. When one student leaves the class the average weight reduces by 100 g. What is the weight of the student who left the class ?
Correct Answer

(C) 49.9 kg.

Explanation

Solution: According to the question, The average weight of 50 students was = 45 kg When one student leaves the class the average reduced by 100 gm. ∴ Total weight reduction due to 49 students = 49 × 100 = 4900 gm = 4.9 kg ∴ The weight of student who left = 45 + 4.9 = 49.9 kg