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Question

The graph between two temperature scales A and B is shown in figure. Between upper fixed point and lower fixed point, there are 150 equal divisions on scale A and 100 on scale B. The relationship for conversion between the two scales in given by:
740594_4de2e838ff974d98b2bfb0fb77fce917.png

A
tA180100=tB150
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B
tA30150=tB100
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C
tB180150=tA100
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D
tB40100=tA180
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Solution

The correct option is C tA30150=tB100
A correct answer is an option(B).
The temperature on one scale can be converted into other scales by using the following identity.
Reading on any scaleLFPUFPLFP = Constant for all scales
where LFP is a Lower fixed point and UFP is Upper fixed point
From the graph, it is clear that the lowest point for the scale A is 30° and the highest point for scale A is 180°.
The lowest point for scale B is 0° and the highest point for scale B is 100°. Hence, the relation between the two scales A and B is given by
tA(LFP)A(UFP)A(LFP)A=tB(LFP)B(UFP)B(LFP)B

tA3018030=tB01000

tA30150=tB100

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