# The Sum of Two Numbers is 18. the Sum of Their Reciprocals is 1/4. Find the Numbers. - Mathematics

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

#### Solution

Let one of the number be then other number is (18 - x).

Then according to question,

1/x+1/(18-x)=1/4

rArr(18 - x+x)/(x(18-x))=1/4

⇒ 18 x 4 = 18x - x2

⇒ 72 = 18x - x2

⇒ x2 - 18x + 72 = 0

⇒ x2 -12x - 6x + 72 = 0

⇒ x(x - 12) - 6(x - 12) = 0

⇒ (x - 6)(x - 12) = 0

⇒ x - 6 = 0

⇒ x = 6

Or

⇒ x - 12 = 0

⇒ x = 12

Since, x being a number,

Therefore,

When x = 12 then another number will be

18 - x = 18 - 12 = 6

And when x = 6 then another number will be

18 - x = 18 - 6 = 12

Thus, the two numbers are 6 and 12.

Concept: Solutions of Quadratic Equations by Factorization
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#### APPEARS IN

RD Sharma Class 10 Maths