Average - Study Mode

[#411] The average weight of first 11 persons among 12 persons is 95 kg. The weight of 12 th person is 33 kg more than the average weight of all the 12 persons. The weight of the 12 th person is :
Correct Answer

(B) 131

Explanation

Solution: Let the average weight of 12 person is = x and weight of 12 persons According to the question, $$eqalign{
& Rightarrow frac{{11 imes 95 + x + 33}}{{12}} = x cr
& Rightarrow 1045 + x + 33 = 12x cr
& Rightarrow 11x = 1078 cr
& Rightarrow x = 98 cr} $$ ∴ The weight of 12 th person is = 98 + 33 = 131 kg

[#412] In the afternoon, a student read 100 pages at the rate of 60 pages per hour. In the evening, when she was tired, she read 100 more pages at the rate of 40 pages per hour. What was her average rate of reading the pages per hours ?
Correct Answer

(C) 48

Explanation

Solution: According to the question, Afternoon 100 pages read at the rate 60 pages per hour Total time taken to read 100 pages = $$frac{100}{60}$$ = $$frac{5}{3}$$ hours Evening 100 pages read at the rate 40 pages per hour Total time taken to read 100 pages = $$frac{100}{40}$$ = $$frac{5}{2}$$ hours Average rate of reading the pages per hour $$eqalign{
& = frac{{200}}{{frac{5}{3} + frac{5}{2}}} cr
& = frac{{200 imes 6}}{{10 + 15}} cr
& = frac{{200 imes 6}}{{25}} cr
& = 48 cr} $$

[#413] The average of 9 observations was found to be 35. Later on, it was detected that an observation 81 was misread as 18. The correct average of the observation is -
Correct Answer

(B) 42

Explanation

Solution: Difference = 81 - 18 = 63 So, change in average = $$frac{+ 63}{9}$$ = + 7 Correct average = 35 + 7 = 42

[#414] Out of 20 boys, 6 are each of 1 m 15 cm height, 8 are of 1 m 10 cm and rest of 1 m 12 cm. The average height of all of them is :
Correct Answer

(A) 1 m 12.1 cm

Explanation

Solution: According to the question, Height of 6 persons = 6 × 1 m 15 cm = 6 m 90 cm Height of 8 persons = 8 × 1 m 10 cm = 8 m 80 cm Height of 6 persons = 6 × 1 m 12 cm = 6 m 72 cm Total Height of 20 persons = 22 m 42 cm Average = $$frac{{22{ ext{ m }}42{ ext{ cm}}}}{{20}}$$ xa0 = 1 m 12.1 cm

[#415] The average of the largest and smallest 3 digits numbers formed by 0, 2 and 4 would be :
Correct Answer

(A) 312

Explanation

Solution: According to the question, Largest number = 420 Smallest number = 204 Average = $$frac{420 + 204}{2}$$ = $$frac{624}{2}$$ = 312