A two digit number is such that the product of its digits is 35 When 18 is added to - Maths -

Question

A two digit number is such that the product of its digits is 35
When 18 is added to the number, the digits interchange their places
Find the number

Ajanta Trivedi · Accepted Answer

let the unit digit be x and the tenth digit be y.

therefore the product of the digits xy= 35......(1)

the number is 10y+x.

if the digits interchange their position the number becomes 10x+y

therefore

$10 y + x + 18 = 10 x + y 9 x - 9 y = 18 x - y = 2........... (2)$

from (1) y=35/x, substitute in (1)

$x - \frac{35}{x} = 2 x^{2} - 35 = 2 x x^{2} - 2 x - 35 = 0 x^{2} - 7 x + 5 x - 35 = 0 (x - 7) (x + 5) = 0$

therefore x=7 or x=-5

since the digits cannot be negative. x=7

from (1) : y=35/7=5

thus the number is 57.

hope this helps you.

cheers!!

A two digit number is such that the product of its digits is 35. When 18 is added to the number, the digits interchange their places. Find the number.