The product of the digits of a two-digit numb | vedclass

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

Question

(D) Let the tens digit be $x$ and the units digit be $y$. The number is $10x + y$.Given that the product of the digits is $14$,so $xy = 14$.When the d

Vedclass · Accepted Answer

$27$

Vedclass · Answer

(D) Let the tens digit be $x$ and the units digit be $y$. The number is $10x + y$.Given that the product of the digits is $14$,so $xy = 14$.When the digits are interchanged,the new number is $10y + x$.According to the problem,the new number is $45$ more than the original number:$(10y + x) - (10x + y) = 45$$9y - 9x = 45$$y - x = 5$,which implies $y = x + 5$.Substitute $y = x + 5$ into $xy = 14$:$x(x + 5) = 14$$x^2 + 5x - 14 = 0$$(x + 7)(x - 2) = 0$Since $x$ must be a positive digit,$x = 2$.Then $y = 2 + 5 = 7$.The original number is $10(2) + 7 = 27$.

The product of the digits of a two-digit number is $14$. The number obtained by interchanging the digits is $45$ more than the original number. Find the original number.

Similar Questions

The roots of the quadratic equation $3x^2 - 4x + 1 = 0$ are:

Solve the following equation using the method of factorization: $\frac{x^{2}-1}{x^{2}+1}=\frac{7}{9}$

Find the roots of the following quadratic equation by using the quadratic formula,if they exist: $2 y^{2}+5 y-3=0$.

The roots of the quadratic equation $x + \frac{2}{x} = 3$ are $\dots$ $(x \neq 0)$.

Solve the following equation using the method of factorization and write its solution set: $\frac{x+1}{x-1} + \frac{x-2}{x+2} = 3$

Vedclass Test Series

Exam Paper Generator

Online Exam Module