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

Obtain the roots of the following quadratic equation by using the general formula for the solution: $2x^{2} - 2\sqrt{2}x + 1 = 0$.

Examine whether the following equation is quadratic or not: $(x-3)(2x+1) = x(x+5)$

Find the discriminant of the following quadratic equation and hence determine the nature of the roots of the equation: $4x^{2} + 12x + 9 = 0$.

Which of the following polynomials does not have any real zero?

Solve the equation $x^{2}-8x-21=0$ using the quadratic formula.

Vedclass Test Series

Exam Paper Generator

Online Exam Module