Average - Study Mode
[#56] The average of the first five multiples of 3 is-
Correct Answer
(B) 9
Explanation
Solution: Average $$eqalign{
& = frac{{3left( {1 + 2 + 3 + 4 + 5}
ight)}}{5} cr
& = frac{{45}}{5} cr
& = 9 cr} $$
[#57] The average of X 1 , X 2 and X 3 is 14. Twice the sum of X 2 and X 3 is 30. What is the value of X 1 ?
Correct Answer
(D) 27
Explanation
Solution: $$eqalign{
& {{ ext{X}}_1} + {{ ext{X}}_2} + {{ ext{X}}_3} cr
& = left( {14 imes 3}
ight) cr
& = 42 cr} $$ According to the question, $$eqalign{
& 2left( {{{ ext{X}}_2} + {{ ext{X}}_3}}
ight) = 30 cr
& Rightarrow {{ ext{X}}_2} + {{ ext{X}}_3} = 15 cr
& herefore {{ ext{X}}_1} = left( {42 - 15}
ight) = 27 cr} $$
[#58] The weight of a person was entered incorrectly as 83 kg instead of 63 kg. As a result, the average weight of a group of people increased by 500 gm. What is the total number of people in the group?
Correct Answer
(C) 40
Explanation
Solution: Let, number of peoples in group = x Average = n ⇒ nx - 63 + 83 = n(x + 500 gm) ⇒ nx + 20 = nx + $$frac{{ ext{n}}}{2}$$ kg ⇒ n = 20 × 2 ⇒ n = 40 OR $$eqalign{
& { ext{Average}} = frac{{{ ext{Sum}}}}{{{ ext{Number}}}} cr
& 500,{ ext{gm}} = frac{{20}}{n} cr
& frac{1}{2} = frac{{20}}{n} cr
& n = 40 cr} $$
[#59] The average of 18 numbers is 37.5. If six numbers of average x are added to them, then the average of all the numbers increases by one. The value of x is:
Correct Answer
(C) 41.5
Explanation
Solution: After added 6 numbers, total numbers will be = 24 Now, the average of 24 numbers = 38.5 Increase '1' in every numbers So, total increasation = 24 The average of 6 numbers (x) = 37.5 + $$frac{{24}}{6}$$ x = 37.5 + 4 x = 41.5
[#60] The average of 44 consecutive odd numbers is 144. What is the largest number?
Correct Answer
(C) 187
Explanation
Solution: Let the number is x, x + 2, x + 4, . . . . . . x + 86 Total value of 44 number is = 44x + 2 + 4 + . . . . . . 86 Value of 2 + 4 + 6 + . . . . . . 86 = 2(1 + 2 + 3 . . . . . . + 43) = $$2left( {frac{{n imes left( {n + 1}
ight)}}{2}}
ight)$$ = 43 × 44 = 1892 According to the question, 1892 + 44x = 144 × 44 44x = 144 × 44 - 1892 x = $$frac{{44left( {144 - 43}
ight)}}{{44}}$$ x = 101 Largest number = 101 + 86 = 187