The sum of digits of a two-digit number is 10. When the digits are reversed, the number decreases by 54. Find the changed number.
Let say, the number is 'ab'.
So,the number is=(10a+b).
According to the question,
$$a+b=10.$$................(1)
when digits are reversed ,the number would become 'ba', which is (10b+a).
So,$$10b+a=10a+b-54.$$
or,$$9a-9b=54.$$
or,$$a-b=6.$$..................(2)
Add (1) and (2) :
$$2a=16.$$
$$a=8.$$
So,b=2.
Original number is 82.
So, the changed number is 28.
B is correct choice.
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