Question

The product of digits of a two digit number is 24. When 18 is added to the number, the digits interchange their places. Determine the number.

Answer 1

Let the ten’s digit of the number be x.
A.T.Q
Product of the digits= 24

Tens digit ×  units digit = 24

Units digit = 24/x

Two digit number= 10x + 24/x


After interchanging the places:

10 × 24/x + x


It is given that if 18 is added to the number the digit get interchange.

10x + 24/x +18 = 10 × 24/x + x

10x² + 24 + 18x = 240 + x²

[Multiplying by x]

10x² - x² +18x = 240 -24

9 x² +18x = 216

9x² + 18x -216= 0

[ Divide by 9]

x² + 2x - 24= 0

x² + 6x - 4x -24= 0

x(x+6) - 4( x+6)= 0

(x+6) ( x-4)= 0

x+6= 0 or x-4= 0

x= -6 or x= 4

But a digit  can never be negative .

so x = 4


 2 digit number= 10x + 24/x


= 10 × 4 + 24/4
= 40 + 6
= 46

Hence, the required 2 digit number= 46

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Hope this will help you...

Answer 2

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