If a two-digit number has a digit sum of 9 and adding 27 reverses its digits, determine the unit digit of the number.
6
Let the tens digit be \(t\) and the unit digit be \(u\), so the number is \(10t + u\).
Given the digit sum: \(t + u = 9\).
Reversing the digits gives \(10u + t\). Adding 27 to the original number produces the reversed number: \((10t + u) + 27 = 10u + t\).
Simplify: \(27 = 9u - 9t = 9(u - t)\), so \(u - t = 3\).
Solve the two equations \(t + u = 9\) and \(u - t = 3\): adding them gives \(2u = 12\), so \(u = 6\) and \(t = 3\).
Check: the number is 36, its reverse is 63, and \(36 + 27 = 63\). Correct.
Hence, the unit digit of the number is 6.
Similar Questions
- If $x + \frac{1}{x} = 2$, then the value of $x^{2} + \frac{1}{x^{2}} = ?$
- If $x + y + z = 0$, then what will be the value of $\frac{x^2}{yz} + \frac{y^2}{zx} + \frac{z^2}{xy}$ ?
- If $x^3 + \frac{1}{x^3} = 18$, then what will be the value of $x + \frac{1}{x}$?
- If the sum of three numbers is zero, then which of the options below will always be equal to the value of the sum of the cubes of those numbers?
- If $x^2 = y+z, y^2 = z+x$ and $z^2 = x+y$, then find the value of $\frac{1}{x+1} + \frac{1}{y+1} + \frac{1}{z+1}$.
- If $x - \frac{1}{x} = 5$, find the value of $x^4 + \frac{1}{x^4}$.
- If $x^4 + \frac{1}{x^4} = 322$ and $x > 1$, then what is the value of $x^3 - \frac{1}{x^3}$?
- 1200 apples were distributed among a group of boys. Each boy got thrice many of the apples as the number of boys in that group. The number of boys in the group was:
- If $x + \frac{1}{x} = 4$, then find the value of $x^2 + \frac{1}{x^2}$
- If $3a + 4b = 2$ and $ab = \frac{1}{36}$, then $27a^3 + 64b^3$ is:
Important Questions from Algebra
In the given question, two equations numbered l and II are given. Solve both the equations and mark the appropriate answer.
I. x2 – 26x + 165 = 0
II. y2 – 38y + 357 = 0
Factorize the following:
(x 2- 6xy + 9y 2) - 25
If P and Q are the points on the line Joining A(-2, 5) and B(3, 1) such that
AP = PQ = QB, then the mid point of PQ is
If a number and its reciprocal added it becomes 6, then what will be sum of its square and square of its reciprocal?
If 3x + 2y = 15, and xy = 6. Find the value of (3x3/2) + (4y3/9).
