Average - Study Mode

[#241] In a class with a certain number of students, if one student weighting 50 kg is added then the average weight of the class increased by 1 kg. If one more student weighting 50 kg is added, then the average weight of the class increased by 1.5 kg over the original average. What is the original average weight (in kg) of the class?
Correct Answer

(D) 47

Explanation

Solution: Let the original average weight of the class be x kg and let there be n students. Then, sum of weights of n students = (nx) kg $$eqalign{
& herefore frac{{nx + 50}}{{n + 1}} = x + 1 cr
& Rightarrow nx + 50 = left( {n + 1}
ight)left( {x + 1}
ight) cr
& Rightarrow nx + 50 = nx + x + n + 1 cr
& Rightarrow x + n = 49 cr
& Rightarrow 2x + 2n = 98.....(i) cr
& { ext{And,}} cr
& Rightarrow frac{{nx + 100}}{{n + 2}} = x + 1.5 cr
& Rightarrow nx + 100 = left( {n + 2}
ight)left( {x + 1.5}
ight) cr
& Rightarrow nx + 100 = nx + 1.5n + 2x + 3 cr
& Rightarrow 2x + 1.5n = 97.....(ii) cr} $$ Subtracting (ii) from (i), we get: 0.5n = 1 or n = 2 Putting n = 2 in (i), we get: x = 47

[#242] The average height of 25 boys is 1.4 m. When 5 boys leave the group, then the average height increased by 0.15 m. What is the average height of the 5 boys who leave ?
Correct Answer

(A) 0.8 m

Explanation

Solution: Sum of height of the 5 boys = (25 × 1.4 - 20 × 1.55) m = 4 m ∴ Required average = $$left( {frac{4}{5}}
ight)$$ = 0.8 m

[#243] The average monthly income of a family of four earning members was Rs. 15130. One of the daughters in the family got married and left home, so the average monthly income of the family came down to Rs. 14660. What is the monthly income of the married daughter?
Correct Answer

(C) Rs. 16540

Explanation

Solution: Monthly income of the married daughter = Rs. (15130 × 4 - 14660 × 3) = Rs. (60520 - 43980) = Rs. 16540

[#244] The average marks obtained by 22 candidates in an examination are 45. The average marks of the first ten are 55 and that of the last eleven are 40. The number of marks obtained by the 11 th candidates is-
Correct Answer

(A) 0

Explanation

Solution: Mark obtained by the 11th candidate = [(45 × 22) - (55 × 10 + 40 × 11)] = (990 - 990) = 0

[#245] The average of 10 numbers is 40.2. Later it is found that two numbers have been wrongly added. The first is 18 greater than the actual number and the second number added is 13 instead of 33. Find the correct average.
Correct Answer

(B) 40.4

Explanation

Solution: Correct sum = (40.2 × 10 - 18 + 33 - 13) = 404 ∴ Correct average = $$left( {frac{{404}}{{10}}}
ight)$$ = 40.4