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Answer:
34
Step-by-step explanation:
Let the units place be x
Let the tens place be y
Therefore, the no is 10y + x.
The reversed no will be 10x + y.
(Explanation: Let us take 43 as an example. It can be written as 4 x 10 + 3 x 1. Hence we take 10y for the tens place.)
Given that
No exceeds 4 times the sum of digits by 6.
The sum of digits is x + y. Therefore the eqn is
10y + x - 4(x + y) = 6
10y + x -4x -4y = 6
6y - 3x = 6
2y - x = 2 (eqn 1)
From condition 2,
10x + y = 10y + x + 9
9x -9y = 9
x - y = 1 (eqn 2)
Adding eqn 1 and 2 by elimination of x
y = 3
Substitute in eqn 2
x = 4
Therefore the number is 10y + x = 30 +4 = 34.
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