Question

The product of digits of a two digit number is 21 and when 36 is subtracted from the number, the digits interchange their places. What is the number?

(a) -24

(b) 42

(c) 73

(d) -37

I have been asked this question in an internship interview.

My doubt is from Solution of Quadratic Equation by Factorisation in chapter Quadratic Equation of Mathematics – Class 10

Answer 1

Right choice is (c) 73

The explanation is: Let the units place of the two digit number be x and the tens place be y.

Product of the digits of the places = 21

xy=21

y=\(\frac {21}{x}\)

Now, the number will be 10y+x

If 36 is subtracted from the number the digits interchange their places.

New number = 10x+y

10y+x-36=10x+y

9y-9x=36

y-x=4

Now, y=\(\frac {21}{x}\)

\(\frac {21}{x}\)-x=4

21-x^2=4x

x^2+4x-21=0

x^2+7x-3x-21=0

x(x+7)-3(x+7)=0

(x+7)(x-3)=0

x = -7, 3

The number is 73.