CLAT CLAT Solved Paper-2018

The number of children in a camp is x and their average weight is 20 kg. If 5 children each weighing 12 kg, join the camp or if 10 children each weighing 21kg leave the camp, the average weight in both the cases remain the same. The value of x is

A) 18

B)        16

C) 15

D)                    14

Correct Answer: C

Solution :

Sol.

Number of children in camp = x

Total weight of children = 20x

Now according to question,

Average when 5 children of weight 12 kg join the

the camp

\[=\frac{20x+60}{x+5}\]

And average when 10 children of weight 21 kg leave the camp

\[=\frac{20x-210}{x-10}\]

\[\Rightarrow \,\frac{20x+60}{x+5}\,=\,\frac{20x-210}{x-10}\]

\[\begin{align} & \Rightarrow \,20{{x}^{2}}\,+60x\,-200x\,-600\,=200{{x}^{2}} \\ & -210x+100x-1050 \\ & -140x-600=-100x-1050 \\ \end{align}\]

\[30x=450\Rightarrow x=15\]