The average mass of class is 52.5 if the average mass of the boy only in class is 50kg and that of girls is only is 54kg find ratio of number of boys to that of girls in class
Let the number of boys in the class be 'x' and the number of girls be 'y'.
Given that the average mass of the class is 52.5 kg, we can write the equation:
(50x + 54y)/(x + y) = 52.5
Multiplying both sides of the equation by (x + y):
50x + 54y = 52.5(x + y)
Expanding and rearranging the equation:
50x + 54y = 52.5x + 52.5y
52.5y - 54y = 52.5x - 50x
-1.5y = 2.5x
Dividing both sides by -1.5:
y = (2.5/1.5)x
The ratio of the number of boys to girls is therefore:
x : y = x : (2.5/1.5)x = 1.5 : 2.5
Simplifying the ratio:
x : y = 3 : 5
Therefore, the ratio of boys to girls in the class is 3 : 5.
To find the ratio of the number of boys to that of girls in the class, we need to compare their average masses.
Let the number of boys in the class be B, and the number of girls in the class be G.
The total mass of the boys in the class would then be 50 * B (as the average mass of the boys is 50kg), and the total mass of the girls would be 54 * G (as the average mass of the girls is 54kg).
We know that the average mass of the class is 52.5kg, which means the total mass of the class is 52.5 * (B + G).
From this, we can set up the following equation:
50 * B + 54 * G = 52.5 * (B + G)
Simplifying this equation:
50B + 54G = 52.5B + 52.5G
54G - 52.5G = 52.5B - 50B
1.5G = 2.5B
Dividing both sides by 1.5:
G = (2.5/1.5)B
Simplifying further:
G = (5/3)B
Therefore, the ratio of the number of boys to that of girls in the class is 3:5.