QQuestion
The difference of two natural numbers is 5 and sum of their reciprocals is \frac{3}{10}. Find the two numbers.
ICSEClass XMathematicsQuadratic Equations04 Mark2026 Easy
✓Answer
Let the numbers be x and x + 5.
\frac{1}{\mathrm{x}}+\frac{1}{\mathrm{x}+5}=\frac{3}{10}⇒ \frac{2\mathrm{x}+5}{\mathrm{x}(\mathrm{x}+5)}=\frac{3}{10}
⇒ 10(2x + 5) = 3x(x + 5)
⇒ 20x + 50 = 3x² + 15x
⇒ 3x² − 5x − 50 = 0
⇒ 3x² + 10x − 15x − 50 = 0
⇒ x(3x + 10) − 5(3x + 10) = 0
⇒ (x − 5)(3x + 10) = 0
x = 5 or x = \frac{-10}{3}
Since x is natural, x = 5.
The other number = x + 5 = 10.
Therefore, the numbers are 5 and 10.
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