The sum of two digits of a 2-digit number is 9. If the number obtained by interchanging the digits exceeds the original number by 27, find the number.
36
Let the number be \(10a+b\) with \(a+b=9\).
Interchanged number minus original: \((10b+a)-(10a+b) = 9(b-a) = 27 \Rightarrow b-a=3\).
Solving \(a+b=9\) and \(b-a=3\): \(b=6,\ a=3\).
Hence, the number is 36.
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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).
