Question

A two digit number is seven times the sum of its digits and is also equal to 12 use of than 3 times the product of its digits . Find the numbers ?​

Answer 1

CORRECT QUESTION :-

A two digit number is seven times the sum of its digits and is also

equal to 12 less than 3 times the product of its digits. Find the numbers ?

SOLUTION :-

Let,

Digit in ten's place = x

Digit on one's place = y

Two digit number = 10x + y

According to the first condition,

$\longrightarrow\sf 10x+y = 7(x+y)\\\\\longrightarrow 10x+y = 7x+7y \\\\\longrightarrow 10x-7x = 7y-y \\\\\longrightarrow 3x= 6y \\\\\longrightarrow x = 2y \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ .......................(1)$

According to the second condition,

$\longrightarrow\sf 10x+y = 3xy-12 \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ .......................(2)$

Substitute x = 2y in equation (2),

$\longrightarrow\sf 10(2y)+y = 3\times 2y\times y -12 \\\\\longrightarrow 20y+y= 6y^2-12 \\\\\longrightarrow 21y= 6y^2-12 \\\\\longrightarrow 6y^2-21y-12 =0\\\\\longrightarrow 2y^2-7y-4 = 0 \\\\\longrightarrow 2y^2-8y+y-4 = 0 \\\\\longrightarrow 2y(y-4)+1(y-4)=0\\\\\longrightarrow (2y+1)(y-4)=0$

y = 4

2y = 8 = x

Two digit number = 84