Question

the sum of the digits of a two-digit number is 6. eight times of this number is 14 times the number obtained by reversing the order of the digits . find the two equations​

Answer 1

Answer :-

Let the digits be x and y

According to the question -

Sum of digits = 6

➩ $\rm x + y = 6 \:\:\:\:\:\:\:\:\: i$

8 times of number = 14 times number obtained by reversing the digits

➩ $\rm 8 ( 10x + y ) = 14 ( 10y + x ) \:\:\:\:\:\:\:\:\: ii$

Solving the equation -

➩ $\rm 80x + 8y = 140y + 14x$

➩ $\rm 80x - 14x = 140y - 8y$

➩ $\rm 66x = 132y$

➩ $\rm x = 2y \:\:\:\:\:\:\:\:\: iii$

Substituting the value of x from equation iii

$\rm x + y = 6$

➩ $\rm 2y + y = 6$

➩ $\rm 3y = 6$

➩ $\rm y = \frac{6}{3}$

➩ $\boxed{\rm y = 2}$

Substituting the value of y in equation i

$\rm x + y = 6$

➩ $\rm x + 2 = 6$

➩ $\rm x = 6 - 2$

➩ $\boxed{\rm x = 4}$

Hence, the number is 42

Answer 2

Answer :-

Let the digits be x and y

According to the question -

Sum of digits = 6

➩ $\rm x + y = 6 \:\:\:\:\:\:\:\:\: i$

8 times of number = 14 times number obtained by reversing the digits

➩ $\rm 8 ( 10x + y ) = 14 ( 10y + x ) \:\:\:\:\:\:\:\:\: ii$

Solving the equation -

➩ $\rm 80x + 8y = 140y + 14x$

➩ $\rm 80x - 14x = 140y - 8y$

➩ $\rm 66x = 132y$

➩ $\rm x = 2y \:\:\:\:\:\:\:\:\: iii$

Substituting the value of x from equation iii

$\rm x + y = 6$

➩ $\rm 2y + y = 6$

➩ $\rm 3y = 6$

➩ $\rm y = \frac{6}{3}$

➩ $\boxed{\rm y = 2}$

Substituting the value of y in equation i

$\rm x + y = 6$

➩ $\rm x + 2 = 6$

➩ $\rm x = 6 - 2$

➩ $\boxed{\rm x = 4}$

Hence, the number is 42