Question

On an X temperature scale, water freezes at $-{125.0}^{\circ }$X and boils at ${375.0}^{\circ }$X. On a Y temperature scale, water freezes at $-{70.0}^{\circ }$Y and boils at $-{30.0}^{\circ }$Y. The value of temperature on X scale equal to the temperature of ${50.0}^{\circ }$Y on Y scale is:

• A. ${455.0}^{\circ }$X
• B. ${125.0}^{\circ }$X
• C. ${1500.0}^{\circ }$X
• D. ${1375.0}^{\circ }$X

Answer 1

The correct option is D

${1375.0}^{\circ }$X

Notice that for both the scales we're using the same liquid i.e. water
$\therefore$ For the same temperature in both the scale, the percentage expansion is same
Given in Y scale, $T={50}^{\circ }$Y
Let the equivalent temperature in X-scale be 'x'
$\frac{X-(-125)}{375-(-125)}=\frac{50-(-70)}{-30-(-70)}\Rightarrow X={1375}^{\circ }X\frac{X-X_i}{X_f-X_i}=\frac{Y-Y_i}{Y_f-Y_i}$
For scale conversions!