Question

The average weight of $39$ students in a class is $23$kgs. Among them Sita is the heaviest while Tina is the lightest. If both of them are excluded from the class still the average remains same. The ratio of weight of Sita to Tina is $15:8$,then what is the weight of the Tina?

Answer 1

Tina's weight $=16$ kilogram.

Suppose the weight of Sita is $x$ kilogram

.weight of Tina is $y$ kilogram

Given that, ratio of Sita and Tina's weight is $15:8$

So,$\frac{x}{y}=\frac{15}{8}$ ........$\left(1\right)$

Combined weight of Sita and Tina $=x+y$

$x+y=$ Average weight $\times$Number of persons

$x+y=23\times (39-37)=23\times 2=46$

By solving both the equation:$x+y=46$ ......$\left(2\right)$ we get

From $\left(2\right)$ we have $x+y=46$

$\Rightarrow y(\frac{x}{y}+1)=46$

$\Rightarrow y(\frac{15}{8}+1)=46$ from $\left(1\right)$

$\Rightarrow \frac{23y}{8}=46$

$\Rightarrow y=46\times \frac{8}{23}=2\times 8=16$

$\therefore y=16$kgs and we have from $\left(2\right)x+y=46$

$\Rightarrow x=46-y=46-16=30$kgs

Hence, weight of Tina is $16$kgs