Average - Study Mode

[#251] If the average weight of 6 students is 50 kg. If two student of average weight of 51 kg are added and two other students of average weight of 55 kg are also added then the average weight of all the students is :
Correct Answer

(D) 51.2 kg

Explanation

Solution: According to the question, Required Average $$eqalign{
& = frac{{6 imes 50 + 51 imes 2 + 55 imes 2}}{{10}} cr
& = frac{{300 + 212}}{{10}} cr
& = frac{{512}}{{10}} cr
& = 51.2{ ext{ Kg}} cr} $$

[#252] The average of the squares of first ten natural numbers is-
Correct Answer

(D) 38.5

Explanation

Solution: As we know that average of square of "n" natural number is $$eqalign{
& = frac{{nleft( {n + 1}
ight)left( {2n + 1}
ight)}}{{6n}} cr
& = frac{{left( {n + 1}
ight)left( {2n + 1}
ight)}}{6} cr} $$ According to the question, Average of square of first ten natural number is $$eqalign{
& = frac{{left( {10 + 1}
ight)left( {20 + 1}
ight)}}{6} cr
& = frac{{11 imes 21}}{6} cr
& = 38.5 cr} $$

[#253] The average of 11 results is 50. If the average of the first six results is 49 and that of the last six is 52, the sixth number is -
Correct Answer

(D) 56

Explanation

Solution: According to the question, Average of 11 numbers is = 50 sum of 11 numbers is = 50 × 11 = 550 ∴ VI number = 312 + 294 - 550 = 56

[#254] A man bought 13 articles at Rs. 70 each, 15 at Rs. 60 each and 12 at Rs. 65 each. The average price per article is -
Correct Answer

(B) Rs. 64.75

Explanation

Solution: According to the question, $$eqalign{
& = frac{{13 imes 70 + 15 imes 60 + 12 imes 65}}{{40}} cr
& = frac{{910 + 900 + 780}}{{40}} cr
& = frac{{2590}}{{40}} cr
& = 64.75 cr} $$

[#255] The average of the three numbers x, y and z is 45. x is greater than the average of y and z by 9. The average of y and z is greater than y by 2. Then the difference of x and z is :
Correct Answer

(C) 7

Explanation

Solution: According to the question, $$eqalign{
& Rightarrow frac{{x + y + z}}{3} = 45 cr
& Rightarrow x + y + z = 135.....(i) cr
& Rightarrow x = frac{{y + z}}{2} + 9 cr
& Rightarrow 2x - y - z = 18.....(ii) cr
& x + y + z = 135 cr
& underline {2x - y - z = 18} cr
& 3x = 153 cr
& x = 51 cr} $$ From (i) y + z = 135 - 51 = 84.....(iii) Also, $$eqalign{
& Rightarrow frac{{y + z}}{2} = y + 2 cr
& Rightarrow y + z = 2y + 4 cr
& Rightarrow z - y = 4 cr
& + y + z = 84 cr
& underline { - y + z = 4} cr
& ,,,,,,,,,2z = 88 cr
& ,,,,,,,,,,,,z = 44 cr} $$ Required difference = 51 - 44 = 7