Question

a two digital​ number is such that the product of its digit is 18 .when 63 is subtracted from the number the digits interchange their places.find the numbers??

Answer 1

ans . the number is 92(29)

Answer 2

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

Unit digit be t

Tens digit be p

Situation,

pt = 18 ................. (a)

t = 18/p ................ (1)

Also,

(10p + t) - 63 = 10t + p

9p - 9t = 63

p - t = 7 ................ (2)

Now,

Substitute the value of (1) in (2) :-

p - 18/p = 7

p² - 18 = 7p

p² - 7p - 18 = 0

p² - 9p + 2p - 18 = 0

p(p - 9) + 2(p - 9) = 0

(p - 9) (p + 2) = 0

p - 9 = 0 or p + 2 = 0

p = 9, -2 (Negative value is not applicable)

p = 9

Substitute value of p in (a),

pt = 18

9t = 18

t = 18/9

t = 2

Number = 92