Question

A two digit number is such that the product of its digits
is 8. When 18 is subtracted from the number, the digits interchange their places
and find the number.​

Answer 1

Answer:

plz see the pic

I solved it step by step

number is 42

Answer 2

$\Large{\textbf{\underline{\underline{According\:to\:the\:Question}}}}$

Assumption

$\textbf{\underline{Two\;digit\;number=10p+c}}$

Also

$\textbf{\underline{Product\;of\;Numbers=8}}$

Hence

pc = 8 ... (1)

$\textbf{\underline{Situation}}$

When 18 is subtracted the digits interchange their places

So,

10p + c - 18 = 10c + p

10p + c - 10c - p = 18

9p - 9c = 18

9(p - c) = 18

$\tt{\rightarrow p-c=\dfrac{18}{9}}$

p - c = 2

p = 2 + c ....(2)

$\textbf{\underline{Substitute\;value\;in \;(1)\;we\;get :-}}$

pc = 8

(2 + c)c = 8

2c + c² = 8

c² + 2c - 8 = 0

c² + 4c - 2c - 8 = 0

c(c + 4) - 2(c + 4) = 0

(c - 2) (c + 4) = 0

(c - 2) = 0

c = 2

(c + 4) = 0

c = -4

$\textbf{\underline{Negative\;value\;is\;not\;possible:-}}$

Hence ,

c = 2

$\textbf{\underline{Substitute\;the\;value\;in\;(1)\;we\;get :-}}$

pc = 8

p × 2 = 8

$\tt{\rightarrow p=\dfrac{8}{2}}$

p = 4

p = 4

${\boxed{\sf\:{Needed\;Number}}}$

= 10p + c

= 10(4) + 2

= 40 + 2

$\Large{\boxed{\sf\:{Needed\;Number=42}}}$