Question

two digits number contains the smaller of two digits in the units place . the product pf the digits is 24 and difference is 5. find the number ?

Answer 1

Answer:83

Step-by-step explanation:

Let,

The 2 digit nos. Be x and y

ATQ,

X>Y

So,

X*Y=24...eq1

X-Y=5...eq2

And,

X=5+Y...eq3

Eq 3 in eq 1

We get,

(5+y)y=24

5y+y*y=24

P(x)=y*y+5y-24=0

Factorising p(x),

y*y+ 8y- 3y -24

y(y+8)-3(y+8)

y-3 and y+8

So,

y = 3 or -8

Here,

We neglect negative sign value.

So,

y=3...in eq 1

We get,

x *3=24

x=24/3=8

x=8

Statement:The number is 84

Answer 2

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

Assume

Unit digit place be p

Ten's digit place be t

Original number = 10t + p

Now,.

Situation,

pt = 24 ......... (1)

t - p = 5

t = 5 + p ........... (2)

$\Large{\boxed{\sf\:{Putting\;value\;of\;t\;in(1)}}}$

pt = 24

p (5 + p) = 24

5p + p² = 24

p² + 5p - 24 = 0

p² + 8p - 3p - 24 = 0

p(p + 8) - 3(p + 8) = 0

(p - 3 ) (p + 8) = 0

(p - 3) = 0

p = 3

Also,

(p + 8) = 0

p = -8

p = -8 Not applicable

So,

p = 3

t = p + 5

t = 3 + 5

t = 8

$\Large{\boxed{\sf\:{Number}}}$

= 10t + p

= 10 × 8 + 3

= 80 + 3

= 83

Hence,

$\Large{\boxed{\sf\:{Number = 83}}}$