A two digit number ab is 60% of x. The two-digit number formed by reversing the digits of ab is 60% more than x. Find x.
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Solution :-
According to the question,
10a + b = 60% of x
=> 10a + b = 0.6x _______(i)
10b + a = x + 60% of x
=> 10b + a = x + 0.6x
=> 10b + a = 1.6x _______(ii)
Subtract equation (i) from (ii) we get,
(10b + a) - (10a + b) = 1.6x - 0.6x
=> 10b + a - 10a - b = x
=> 9b - 9a = x
=> x = 9(b - a)
Here, x should be multiple of 9.
10a + b = 0.6x => 10a + b = 3x/5
this implies that x should also multiple of 5 Or, x should be a multiple of 45.
So, ab = 60% of 45 = 27 and ba = 72
Answer : x = 45
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