Q. The sum of two numbers is 18 and the sum of their reciprocals is 1/4 . Find the numbers.

Ans: Let the numbers be X and Y

Step 1: By 1st condition: X + Y = 18

or X = 18 – Y ….. (i)

Step 2: By 2nd condition:

By simplifying this equation, we get:

……. (ii)

Step 3: By substituting value of X from equation (i) in equation (ii), we get:

$4(18 – Y + Y) = (18 – Y) Y

72 = 18 Y – Y²

Y² – 18Y + 72 = 0

Y² – 12 Y – 6Y + 72 = 0

Y(Y – 12) – 6(Y – 12) = 0

(Y – 12) (Y – 6) = 0

Therefore Y = 6 and Y = 12

Step 4: Let’s put value of Y in equation (i), we get:

at Y = 6, X = 18 – 6 = 12

at Y = 12, X = 18 – 12 = 6

Therefore the numbers are 6 and 12

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