In a given scale X, the ice point is 40∘X and the steam point is 120∘X. For another scale Y, the ice point and steam point are −30∘Y and 130∘Y respectively. If X reads 50∘X temperature of a body, then Y would read
A
−5∘C
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B
−8∘C
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C
−10∘C
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D
−12∘C
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Solution
The correct option is C−10∘C Given:
For scale X,
Ice point, TiX=40∘X
Steam point, TsX=120∘X
For scale Y,
Ice point, TiY=−30∘Y
Steam point, TsY=130∘Y
Reading in scale X of temperature of the body, TX=50∘X
To find: Reading in scale Y of temperature of the body, TY=?
We know relation between any two scales are given by - TX−TiXTsX−TiX=TY−TiYTsY−TiY ⇒TX−40120−40=TY−(−30)130−(−30) ⇒50−4080=TY+30160 ∴TY=−10∘Y