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26 Jan 2021, 09:00
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The average age of three groups of people is: Group x = 83 years, Group y = 76 years, Group z = 85years, Group x and y = 79 years and Group y and z = 81years. Find the average age of all the groups.
(A) 82.5 years
(B) 81.5 years
(C) 80.5 years
(D) 79.5 years
(E) 78.5 years
(A) 82.5 years
(B) 81.5 years
(C) 80.5 years
(D) 79.5 years
(E) 78.5 years
26 Jan 2021, 10:00
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Find the ratio of students and then find the average.
Follow the screenshot.
Ans B
Follow the screenshot.
Ans B
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File comment: Edited: The 2nd ratio can be found from both ways i.e 85-81=4
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26 Jan 2021, 14:05
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I´ve found another way. Maybe more complicated but still another option.
You know that the average of X and Y is 79, so you need to calculate:
(83x+76y)/(x+y)=79
It gives you the x:y ratio: 4:3
On the other hand, you have the average of Y and Z, meaning you calculate the same as previous:
(76y+85z)/(y+z)=81
It gives you the y:z ratio, which is 5:4
Combining both, you will realize that the ratio x:y:z is 12:15:20
In detail: 12= 4*3 (x*y), 15= 3*5 (y1*y2) and, finally, 20= 5*4 (y2*z).
The statement is asking you to find the average of x, y and, z. Now you have everything you need to do it:
(83*12+76*15+85*20)/(12+15+20)
Being x=12, y=15 and z=20, as I said before.
This results in 81,5 approx., which is answer B.
You know that the average of X and Y is 79, so you need to calculate:
(83x+76y)/(x+y)=79
It gives you the x:y ratio: 4:3
On the other hand, you have the average of Y and Z, meaning you calculate the same as previous:
(76y+85z)/(y+z)=81
It gives you the y:z ratio, which is 5:4
Combining both, you will realize that the ratio x:y:z is 12:15:20
In detail: 12= 4*3 (x*y), 15= 3*5 (y1*y2) and, finally, 20= 5*4 (y2*z).
The statement is asking you to find the average of x, y and, z. Now you have everything you need to do it:
(83*12+76*15+85*20)/(12+15+20)
Being x=12, y=15 and z=20, as I said before.
This results in 81,5 approx., which is answer B.
