Question

The sum of two numbers is 13 and the sum of their reciprocals is \(\frac {13}{40}\). What are the two numbers?

(a) 76

(b) 49

(c) 58

(d) 94

This question was posed to me during an online interview.

My doubt stems from Solution of Quadratic Equation by Factorisation topic in section Quadratic Equation of Mathematics – Class 10

Answer 1

Correct option is (c) 58

To explain: Sum of the numbers is 13.

Let one number be x. Other number is 13-x.

Sum of their reciprocals = \(\frac {13}{40}\)

\(\frac {1}{x} + \frac {1}{13-x}=\frac {13}{40}\)

\(\frac {13-x+x}{x(13-x)}=\frac {13}{40}\)

\(\frac {13}{13x-x^2}=\frac {13}{40}\)

\(\frac {1}{13x-x^2}=\frac {1}{40}\)

40=13x-x^2

x^2-13x+40=0

x^2-5x-8x+40=0

x(x-5)-8(x-5)=0

(x-8)(x-5)=0

x=8, 5

The number is 58 or 85.