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The mean marks (out of $100$ ) of boys and girls in an examination are $70$ and $73$ , respectively. If the mean marks of all the students in that examination is $71$ , find the ratio of the number of boys to the number of girls.

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1 : 1

1 : 2

2 : 1

2 : 3

answer is B.

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Detailed Solution

It is given,
Mean marks of boys are

= 70

Mean marks of girls are

= 73

Let the total number of boys be

x

and the total number of girls br

y

.
Let the sum of the marks of boys be

a

and the sum of the marks of girls be

b

.
Therefore,

⇒ a x = 70

⇒ a = 70 x

And

⇒ b y = 73

⇒ b = 73 y

Now, mean marks of all the students is

71

.
Therefore,

⇒ s u m o f t h e m a r k s o f a l l t h e s t u d e n t s x + y = 71

Sum of the marks of all the students

= a + b

⇒ a + b = 70 x + 73 y

Therefore,

⇒ 70 x + 73 y x + y = 71

⇒ 70 x + 73 y = 71 x + 71 y

⇒ 2 y = x

⇒ x y = 21

Therefore the ratio is

2 : 1

.
Hence, the correct option is 2.

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