Question

Q.8) On reversing the digits of a two digit number, the number obtained is 9 less than three times the
original number. If the difference of these two numbers is 45, find the original number.​

Answer 1

Answer:

The original number was 27.

Step-by-step explanation:

Let the original number be (10x + y)

Now,

Reversing the number we get, (10y + x)

But, according to the Question,

(10y + x) = 3(10x + y) - 9

10y + x = 30x + 3y - 9

30x - x + 3y - 10y - 9 = 0

29x - 7y - 9 = 0

29x - 7y = 9 ----- 1

Now,

We know that, (10y + x) will be the greater number, because it is 3 times the other number.

So,

(10y + x) - (10x + y) = 45

10y + x - 10x - y = 45

9y - 9x = 45

9(y - x) = 45

y - x = 45/9

y - x = 5

So,

y = 5 + x ----- 2

Putting eq.2 in eq.1 we get,

29x - 7(5 + x) = 9

29x - 35 - 7x = 9

29x - 7x = 35 + 9

22x = 44

x = 44/22

x = 2

Putting x = 2 in eq.2 we get,

y = 5 + 2

y = 7

Thus,

the original number was 10(2) + 7

= 20 + 7

= 27

Hence, 27 was the original number.

Hope it helped and you understood it........All the best