A class consists of $50$ students out of which $30$ are girls. The mean of marks scored by girls in a test is $73$ (out of $100$ ) and that of boys is $71$ . Determine the mean score of the whole class.

72.2

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73.9

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75.6

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78

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Solution

The correct option is D $72.2$
Total number of students= $50$ .
Number of girls= $30$ .
Number of boys= $50 - 30 = 20$ .
Mean marks scored by girls= $73$ .
$\Rightarrow \frac{s u m o f t h e m a r k s o f g i r l s}{n u m b e r o f g i r l s} = m e a n m a r k s s c o r e d b y g i r l s$
$\Rightarrow \frac{s u m o f t h e m a r k s o f g i r l s}{30} = 73$
$\Rightarrow s u m o f t h e m a r k s o f g i r l s = 73 * 30$
$\Rightarrow s u m o f t h e m a r k s o f g i r l s = 2190$

Mean marks scored by boys= $71$ .
$\Rightarrow \frac{s u m o f t h e m a r k s o f b o y s}{n u m b e r o f b o y s} = m e a n m a r k s s c o r e d b y b o y s$
$\Rightarrow \frac{s u m o f t h e m a r k s o f b o y s}{20} = 71$
$\Rightarrow s u m o f t h e m a r k s o f g i r l s = 71 * 20$
$\Rightarrow s u m o f t h e m a r k s o f g i r l s = 1420$

$T o t a l s u m o f m a r k s = 2190 + 1420 = 3610$
$\Rightarrow \frac{T o t a l s u m o f t h e m a r k s}{T o t a l n u m b e r o f s t u d e n t s} = m e a n s c o r e o f t h e w h o l e c l a s s$

$\Rightarrow \frac{3610}{50} = m e a n s c o r e o f t h e w h o l e c l a s s$
$\Rightarrow m e a n s c o r e o f t h e w h o l e c l a s s i s 72.2$

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A class consists of 50 students out of which 30 are girls. The mean of marks scored by girls in a test is 73 (out of 100) and that of boys is 71. Determine the mean score of the whole class.

A class consists of $50$ students out of which $30$ are girls. The mean of marks scored by girls in a test is $73$ (out of $100$ ) and that of boys is $71$ . Determine the mean score of the whole class.