Q. 24

# The sum of two numbers is 16 and the sum of their reciprocals is Find the numbers.

Let the two numbers be x and y.

According to question -

x + y = 16.....(1)

and,  3x + 3y = xy.....(2)

From equation (1), we get -

x = 16 - y.....(3)

Substitute the value of x in equation (2), we get -

3(16 - y) + 3y = (16 - y)y

48 = 16y - y2

y2 - 16y + 48 = 0

y2 - 12y - 4y + 48 = 0

y(y - 12) - 4(y - 12) = 0

(y - 4)(y - 12) = 0

y = 4 or y = 12

Case 1. When y = 4

x = 12 [from equation (3)]

Case 2. When y = 12

x = 4 [from equation (3)]

Thus, the possible values are 12 and 4.

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