Answer-A two-digit number decreases by 54 when its digits are reversed. If the sum of its digits is 10, wha...

Q: Answer-A two-digit number decreases by 54 when its digits are reversed. If the sum of its digits is 10, wha...

For the original number, let the unit digit and tens digit be y and x, respectively.So, the original number 10x yNow, if the digits are reversed, the new number 10y x.ATQ, 10x y 10y x 54Or, 9x 9y 54So, x y 6.iAnd, given that, x y 10iiBy adding equation i and equation ii, we get,2x 16So, x 8And, y 2So, the original number 10x y 10 8 2 80 2 82

Question

Accepted Answer

For the original number, let the unit digit and ten’s digit be ‘y’ and ‘x’, respectively.

So, the original number = (10x + y)

Now, if the digits are reversed, the new number = (10y + x).

ATQ, (10x + y) – (10y + x) = 54

Or, 9x – 9y = 54

So, x – y = 6……….(i)

And, given that, x + y = 10………(ii)

By adding equation (i) and equation (ii), we get,

2x = 16

So, ‘x’ = 8

And, ‘y’ = 2

So, the original number = 10x + y = 10 × 8 + 2 = 80 + 2 = 82

A two-digit number decreases by 54 when its digits are

Solution

Relevant for Exams: