Average - Study Mode

[#291] A set A consists of integers 27, 28, 30 and 33. If integer k is included in the set, the average of set A will increase by 30%. What is the value of integer k ?
Correct Answer

(C) 73.75

Explanation

Solution: Average of set A = $$frac{27 + 28 + 30 + 33}{4}$$ = $$frac{118}{4}$$ = 29.5 After increase = $$frac{29.5 × 130}{100}$$ = 38.35 Now $$frac{{{ ext{Sum of first four numbers + k}}}}{5}$$ xa0 xa0 xa0 $$ = { ext{New average}}$$ ⇒ 118 + k = 38.35 × 5 ⇒ 118 + k = 191.75 ⇒ k = 191.75 - 118 ⇒ k = 73.75

[#292] The average age of 40 students of class is 18 years. When 20 new students are admitted to the same class, the average age of the students of the class is increased by 6 months. The average age of newly admitted students is ?
Correct Answer

(B) 19 years 6 months

Explanation

Solution: According to the question, Average age of 40 students of class is = 18 years Let the average age of 20 new students = x years ∴ $$frac{40 × 18 + 20 × x}{60}$$ xa0 = $$left( {18 + frac{1}{2}}
ight)$$xa0 years ⇒ $$frac{720 + 20x}{60}$$ xa0 = $$frac{37}{2}$$ ⇒ $$frac{720 + 20x}{30}$$ xa0 = 37 ⇒ 20x = 390 ⇒ x = 19.5 ∴ Average age of newly admitted students is = 19.5 = 19 years 6 months

[#293] The mean weight of 34 students of a school is 42 kg. If the weight of the teacher be included, the mean rises by 400 grams. Find the weight of the teacher (in kg.)
Correct Answer

(D) 56 kg

Explanation

Solution: According to the question, Total increase in weight including teacher = 400 × 35 = 14000 gm = 14 kg If the teacher's weight has been '42' kg so there would have not been any change in average weight. ∴ Teacher's weight = 42 + 14 = 56 kg.

[#294] Five years ago, the average age of P and Q was 25. The average age of P, Q and R today is 25. Age of R after 5 years will be :
Correct Answer

(B) 20 years

Explanation

Solution: According to the question, $$frac{P + Q}{2}$$ = 25 P + Q = 50.....(i) (5 years ago) $$frac{P + Q + R}{3}$$ xa0 = 25 P + Q + R = 75.....(ii) (present age) ∴ Present age of P + Q = 50 + 10 = 60 years Present age of R = 75 - 60 = 15 years ∴ Age of R after 5 years = 15 + 5 = 20 years

[#295] A cricketer whose bowling average is 24.85 runs per wickets, takes 5 wickets for 52 runs in next inning and thereby decreases his average by 0.85. The number of wickets taken by him till the last match was :
Correct Answer

(B) 85

Explanation

Solution: Let the number of wickets = x According to question, ⇒ 24.85x + 52 = 24 (x + 5) ⇒ 24.85 x + 52 = 24x + 120 ⇒ 0.85x = 68 ⇒ x = $$frac{69 × 100}{85}$$ ⇒ x = 80 Number of wickets till the last match is = x + 5 = 80 + 5 = 85