Question

Arya takes a number adds \(\frac{13}{3}\) to it and then divides it by 3. At the end of all operations he gets 12. What would be the original number?

(a) \(\frac{23}{3}\)

(b) \(\frac{3}{23}\)

(c) 23

(d) 3

I got this question in a job interview.

I'd like to ask this question from Applications of Linear Equation (Create and Solve the Equations) in chapter Linear Equations in One Variable of Mathematics – Class 8

Answer 1

Correct choice is (a) \(\frac{23}{3}\)

The explanation: Let the number chosen by Arya be x.

The first operation carried out by Arya was adding \(\frac{13}{3}\) to the number.

Hence, the equation formed is x + \(\frac{13}{3}\) = 12

The second operation is to divide throughout by 3.

Hence, the equation is modified to \(\frac{x}{3} + \frac{13}{9}\) = 4

\(\frac{x}{3} + \frac{13}{9}\) = 4

∴ \(\frac{3x}{9} + \frac{13}{9} = \frac{36}{9}\)

∴ 3x + 13 = 36

∴ 3x = 23

∴ x = \(\frac{23}{3}\).