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Among the following options, the number must be subtracted from each of the numbers $10, 12, 19, 24$ to get the numbers which are in proportion?

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answer is C.

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Detailed Solution

Given that the proportional numbers are

10, 12, 19, 24

.
The objective is to find the number that must be subtracted from each of the numbers.
Assume that the number is

x

, apply condition for proportionality,

a b = c d

Substitute the known values within the formula,

10 − x 12 − x = 19 − x 24 − x

By solving the above equation,

240 − 10 x − 24 x + x 2 = 228 − 19 x − 12 x + x 2

By simplification,

240 − 34 x = 228 − 31 x

34 x − 31 x = 240 − 228

3 x = 12 x = 4

Hence the number that must be subtracted from the numbers is 4.
Hence option 3 is correct.

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