Question

On an X temperature scale, water freezes at- 125.0 X and boils at X. On a Y temperature scale . water freeze at - 70.0 Y and boils at - 30.0 Y The value of temperature on X -scale equal to the temperature of 50.0 Y on Y - scale is:

• A. 455.0 X
• B. 250.0 X
• C. 1375.0 X
• D. 1500.0 X

Answer 1

Answer: (B)

250.0 X

Plot the reaction between $X$ and ${}^{o}C$ and $Y$ & ${}^{o}C$ in a $X{-}^{o}C$ graph & $Y{-}^{o}C$ graph

From the graph obtains the equations of straight line using two point method :-

$\frac{x-x_0}{x_1-x_0}=\frac{y-y_0}{y_1-y_0}$ [$(x_0,y_0)\left(x_1{y}_1\right)$ are two points on graph]

That gives,

$\frac{C-O}{100-\theta }=\frac{X+125}{0+125}$ and $\frac{C-0}{100-0}=\frac{Y+70}{-30+70}$

$=C=\frac{4}{5}(X+125)$ and $C=\frac{5}{2}(Y+70)$

comparing both gives,

$\frac{4}{5}(X+125)=\frac{5}{2}(Y+70)$

When $Y=50$ we get :-

$\frac{4}{5}(x+125)=\frac{5}{2}\times 120$

$=x=250$