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Q.

In an examination, the average marks (out of 100) for boys and girls are 70 and 73, respectively. If the average of all students in that examination is 71, what is the ratio of the number of boys to the number of girls?

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a

2:1

b

3:1

c

1:4

d

5:1

answer is A.

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Detailed Solution

Given, in an examination, the average marks (out of 100) for boys and girls are 70 and 73, respectively.
Let the number of boys be x and the sum of the marks of boys is a and the number of girls be y and the sum of the marks of boys be a.
We know that

mean = \frac{Sum of all observations}{Number of observations}

.
So,

\frac{a}{x} = 70

.
a = 70x
And

\frac{b}{y} = 73

b = 73y
The average mark of the total students in that examination is 71.

\frac{a + b}{x + y} = 71

\frac{70 x + 73 y}{x + y} = 71

70x + 73y = 71x + 71y
x = 2y

\frac{x}{y} = \frac{2}{1}

Hence, the ratio of the number of boys to girls is 2:1.
So, option 1 is correct.

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