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May 30 2018
Question Suppose y is equal to the sum of two quantities of which one varies directly as x and the other inversely as x. if y = 6 when x = 4, and y = 10/3 when x = 3, then what is the relation between x and y?

According to the question

y = lx + m/x …..(i)

where l and m are proportionality constant.

When y = 6 and 4, then

6 = 4l + m/4

Therefore, 16l + m = 24 …..(ii)

When y = 10/3,  x = 3, then

10/3 = 3l + m/3

Therefore, 9l + m = 10

On solving eqs. (ii) and (iii), we get

l = 2 and m = -8

from equation (i)

y = 2x – 8/x


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