Question 29

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.

Solution

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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