Question

a two digit number is 5 times the sum of its digits and is also equal to 5 more than twice the product of its digits.find the number.

Answer 1

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

Assumption

Unit digit be t

Tens digit be p

Situation,

10p + t = 5(p + t) .............. (1)

4t = 5p

t = 5p/4 ............................ (2)

Now,

Putting the value of (2) in (1), we get :-

10p + 5p/4 = 2p × 5p/4 + 5

45p/4 = 10p²/4 + 5

10p² - 45p + 20 = 0

2p² - 9p + 4 = 0

2p² - 8p - p + 4 = 0

2p(p - 4) - 1(p - 4) = 0

(p - 4) (2p - 1) = 0

p - 4 = 0 or 2p - 1 = 0

p = 4, 1/2 (Fraction is not acceptable)

p = 4

Putting value of p in (1),

t = 5p/4

t = 5(4)/4

t = 20/4

t = 5

Number = 45

Therefore,

Number = 45