A two-digit number is such that the product o | 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 $xy = 10$.When $27$ is added

Vedclass · Accepted Answer

$25$

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 $xy = 10$.When $27$ is added to the number,the digits are interchanged,so the new number is $10y + x$.According to the problem: $(10x + y) + 27 = 10y + x$.Rearranging the terms: $9x - 9y = -27$,which simplifies to $x - y = -3$ or $y - x = 3$.Substitute $y = x + 3$ into the product equation: $x(x + 3) = 10$.$x^2 + 3x - 10 = 0$.$(x + 5)(x - 2) = 0$.Since $x$ must be a positive digit,$x = 2$.Then $y = 2 + 3 = 5$.The number is $10(2) + 5 = 25$.

$A$ two-digit number is such that the product of its digits is $10$. When $27$ is added to the original number,the new number obtained is the same as the number obtained by interchanging the digits of the original number. Determine the number.

Similar Questions

Five years ago,the sum of the ages of a father and two sons was $x$ years. Then,after five years,the sum of the ages of all will be $\ldots \ldots \ldots$ years.

Solve the following pair of equations by the method of cross-multiplication:
$2x + y = 35$
$3x + 4y = 65$

Find the value$(s)$ of $p$ for the pair of equations $2x + 3y - 5 = 0$ and $px - 6y - 8 = 0$ if the system has a unique solution.

Write an equation of a line passing through the point representing the solution of the pair of linear equations $x+y=2$ and $2x-y=1$. How many such lines can we find?

Solve the following pairs of equations:
$43x + 67y = -24$
$67x + 43y = 24$

Vedclass Test Series

Exam Paper Generator

Online Exam Module