Average age of people in room A and room B is 35 and 30 years, respectively. If the overall average age of people in both the rooms is 31 years, and there are 3 more people in room B than in room A, how many people are there in room B?
Answers
Given :- Average age of people in room A and room B is 35 and 30 years, respectively. If the overall average age of people in both the rooms is 31 years, and there are 3 more people in room B than in room A, how many people are there in room B ?
Solution :-
Let us assume that, total number of people in the room A are x .
So,
→ Total number of people in the room A = x
→ Average age of people in the room A = 35
then,
→ Sum of ages of all people in the room = (Total number) * Average = x * 35 = 35x years.
Similarly,
→ Total number of people in the room B = (x + 3)
→ Average age of people in the room A = 30
then,
→ Sum of ages of all people in the room = (Total number) * Average = (x+3) * 30 = (30x + 90) years.
Also, given that, the overall average age of people in both the rooms is 31 years .
So,
→ Total Number of people in both rooms = x + (x + 3) = (2x + 3)
→ Average = 31 years.
then,
→ Sum of ages of all people in both rooms = 31(2x + 3) = (62x + 93) years.
therefore,
→ Room A + Room B = Total age
→ 35x + (30x + 90) = (62x + 93)
→ 65x + 90 = 62x + 93
→ 65x - 62x = 93 - 90
→ 3x = 3
→ x = 1 .
hence,
→ Number of People in room B = (x + 3) = (1 + 3) = 4 People (Ans.)
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Given : Average age of people in room A and room B is 35 and 30 years, respectively.
overall average age of people in both the rooms is 31 years,
there are 3 more people in room B than in room A,
To Find : how many people are there in room B
Solution :
Let say People in room B are = P
People in room A are = P - 3
Total people in Both rooms = P + P - 3 = 2P-3
Average age of people in room A = 35
People = P - 3
Age in room A = 35(P - 3) = 35P - 105
Average age of people in room B = 30
People = P
Age in room B = 30P
Total Age = 35P - 105 + 30P = 65P - 105
overall average age of people in both the rooms = 31
Total people in Both rooms = 2P-3
Total age = 31(2P - 3) = 62P - 93
65P - 105 = 62P - 93
=> 3P = 12
=> P = 4
People in room B are 4
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