There are $50$ students in a class, of which $40$ are boys. The average weight of the class is $44 k g$ and that of the girls is $40 k g$ . Find the average weight of the boys.

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Solution

Step 1: Find the total weight of class.
$A v e r a g e w e i g h t o f c l a s s = \frac{T o t a l w e i g h t o f c l a s s}{T o t a l n u m b e r o f s t u d e n t s}$
$44 = \frac{T o t a l w e i g h t o f c l a s s}{50}$
$T o t a l w e i g h t o f c l a s s = 50 \times 44 = 2200 k g$
Step 2: Now, we will find the total number of girls and their total weight.
$T o t a l n u m b e r o f g i r l s = T o t a l n u m b e r o f s t u d e n t s - T o t a l n u m b e r o f b o y s$
$T o t a l n u m b e r o f g i r l s = 50 - 40 = 10$
$A v e r a g e w e i g h t o f g i r l s = \frac{T o t a l w e i g h t o f g i r l s}{T o t a l n u m b e r o f g i r l s}$
$40 = \frac{T o t a l w e i g h t o f c l a s s}{10}$
$T o t a l w e i g h t o f g i r l s = 40 \times 10 = 400 k g$
Step 3: Now we will find the total weight of boys and their average weight.
$T o t a l w e i g h t o f b o y s = T o t a l w e i g h t o f s t u d e n t s - T o t a l w e i g h t o f g i r l s$
$T o t a l w e i g h t o f b o y s = 2200 - 400 = 1800 k g$
$A v e r a g e w e i g h t o f b o y s = \frac{T o t a l w e i g h t o f b o y s}{T o t a l n u m b e r o f b o y s}$
$A v e r a g e w e i g h t o f b o y s = \frac{1800}{40} = 45 k g$
Hence, average weight of boys is $45 k g$ .

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