Question

A two digit number is such that the product of its digit is 35 when 18 is added to the number the digits interchange

Answer 1

Solve the equation and you will get your answer..

Hope it helps you.

Answer 2

➤Correct QuestiOn-

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

➤SolutiOn-

${\tt{\text{Let\:x\:and\:y\:be\:the\:digit\:\:at\:tens\:and\:unit\:places\:respectively}}}$

Then two digit number = 10x + y

product of digits = 35

⇒xy = 35.....................(1)

As per given

⇒10x + y + 18 = 10y +x

⇒9x - 9y = - 18

⇒x - y = - 2................(2)

Using (1) and (2) we get,

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

∴x >0 therefore x= 5

Putting this value in equation (1) we get,

⇒y=7

${\bf{\green{Hence,\: required\: number=}}}$

$10x + y = 5 \\ = 5 \times 10 + 7 \\ \boxed{ \red = 57}$