The sum of the digits of a two-digit number i | vedclass

Name: Exam Paper Generator | JEE NEET Paper Generator | Vedclass
Brand: Vedclass
Rating: 5 (35 reviews)

Question

(C) Let the digit at the ten's place be $y$ and the digit at the unit's place be $x$.The original number is $10y + x$.According to the problem,the sum

Vedclass · Accepted Answer

$42$

Vedclass · Answer

(C) Let the digit at the ten's place be $y$ and the digit at the unit's place be $x$.The original number is $10y + x$.According to the problem,the sum of the digits is $6$:$x + y = 6$  ............ $(1)$When the digits are interchanged,the new number is $10x + y$.According to the problem,the new number is $18$ less than the original number:$(10y + x) - (10x + y) = 18$$9y - 9x = 18$Dividing by $9$,we get:$y - x = 2$  ............ $(2)$Adding equation $(1)$ and equation $(2)$:$(x + y) + (y - x) = 6 + 2$$2y = 8$$y = 4$Substituting $y = 4$ into equation $(1)$:$x + 4 = 6$$x = 2$Therefore,the original number is $10(4) + 2 = 42$.

The sum of the digits of a two-digit number is $6$. The number obtained by interchanging the digits is $18$ less than the original number. Find the original number.

Similar Questions

$A$ fraction becomes $\frac{4}{5}$ if $1$ is added to both the numerator and the denominator. If $5$ is subtracted from both the numerator and the denominator,it becomes $\frac{1}{2}$. Find the fraction.

For eliminating $y$ from the equations $3x - 2y = 1$ and $5x + y = 6$,the second equation should be multiplied by

Which of the following is a linear equation in two variables?

Solve the following pair of linear equations in two variables using a graph: $x + y = 8$ and $x - y = 2$.

The pair of equations represented by the above figures is:

Vedclass Test Series

Exam Paper Generator

Online Exam Module