Average - Study Mode

[#346] The average weight of 45 students in a class is 52 kg. Five of them whose average weight is 48 kg leave the class and other 5 students whose average weight is 54 kg join the class. What is the new average weight (in kg) of the class?
Correct Answer

(C) $$52frac{2}{3}$$

Explanation

Solution: Sum of the weights of the students after replacement = [(52 × 45) - (48 × 5) + (54 × 5)] kg = 2370 kg ∴ New average = $$left( {frac{{2370}}{{45}}}
ight)$$ kg = $$52frac{2}{3}$$ kg

[#347] The captain of a cricket team of 11 members is 26 years old and the wicket keeper is 3 years older. If the ages of these two are excluded, the average age of the remaining players is one year less than the average of the whole team. What is the average age of the team?
Correct Answer

(A) 23 years

Explanation

Solution: Let the average age of the whole team be x years. ∴ 11x - (26 + 29) = 9 (x - 1) ⇒ 11x - 9x = 46 ⇒ 2x = 46 ⇒ x = 23 So, the average age of the team is 23 years.

[#348] A motorist travels to a place 150 km away at an average speed of 50 km/hr and returns at 30 km/ hr. His average speed for the whole journey in km/hr is-
Correct Answer

(C) 37.5 km/hr

Explanation

Solution: Average speed $$eqalign{
& = left( {frac{{2xy}}{{x + y}}}
ight){ ext{ km/hr}} cr
& = left( {frac{{2 imes 50 imes 30}}{{50 + 30}}}
ight){ ext{ km/hr}} cr
& = 37.5{ ext{ km/hr}} cr} $$

[#349] The average age of a husband and wife at the time of their marriage was 25 years. A son was born to them two years after their marriage. The present average age of all three of them is 24 years. How many years is it since the couple got married?
Correct Answer

(C) 8 years

Explanation

Solution: Sum of the ages of husband and wife at the time of their marriage = (25 × 2) yrs = 50 yrs Sum of the ages of husband and wife when their son was born = (50 + 2 × 2) yrs = 54 yrs Sum of the ages of husband, wife and son at present = (24 × 3) yrs = 72 yrs ∴ Age of son = $$frac{{left( {72 - 54}
ight)}}{3}$$ xa0 = $$frac{{18}}{3}$$ xa0 = 6 years Hence, the couple got married (6 + 2) = 8 years ago

[#350] The average age of a group of persons going for picnic is 16 years. Twenty new persons with an average age of 15 years join the group on the spot due to which their average age become 15.5 years. The number of persons initially going for picnic is -
Correct Answer

(C) 20

Explanation

Solution: Let the initial number of persons be x. Then, ⇒ 16x + 20 × 15 = 15.5 (x + 20) ⇒ 0.5x = 10 ⇒ x = 20