A certain quantity is measured on two different scales, the R-scale and the S-scale, that are related linearly. Measurements on the R-scale of 6 and 36 correspond to measurements on the S-scale of 30 and 80, respectively. What measurement on the R-scale corresponds to a measurement of 100 on the S-scale?

(A) 20 (B) 36 (C) 48 (D) 60 (E) 84

48. C

Step-by-step explanation:

Since they are related linearly, they follow the relation:

y = mx + c

Hence, let the measurement on the r scale be x and the measurement on the s scale be y.

Now, let's substitute these values in the straight line equation.

For the first measurement, 6 corresponds to 36. Inserting this in the equation:

36 = 6m + c ... (i)

For the second measurement, 36 corresponds to 80.

80 = 36m + c ... (ii)

Solving both simultaneously:

We get m = 10/6 and c = 20

Now, a measurement of what on the r scale corresponds to 100 on the s scale.

100 = 10/6 (m) + 20

Solving this gives 48.