Question

In a two digit number, the sum of digits is 13. If the number is subtracted from the one obtained by interchanging the digits​ the result is 45. What is the number

Answer 1

Answer:

Let’s assume the digit at the unit’s place as x and at ten’s place as y.

Then the required number is 10y + x.

Also it’s given that, the sum of the digits of the number is 13,

So, x + y = 13………… (i)

On interchanging the position of digits, the new number so formed will be 10x+y.

Again is it’s given that, the difference between the new number so formed upon interchanging the digits and the original number is equal to 45.

Therefore, this can be expressed as;

(10x + y) – (10y + x) = 45

⇒ 110x + y – 10y – x = 45

⇒ 9x – 9y = 45

⇒ 9(x – y) = 45 ⇒ x – y = 5………..(ii)

Solving (i) and (ii) we can find x and y,

Now, adding (i) and (ii),

we get;

(x + y) + (x – y) = 13 + 5 ⇒ x + y + x – y = 18

⇒ 2x = 18 ⇒ x = 9

Putting the value of x in the equation (i),

we find y; 9 + y = 13 ⇒ y = 13 – 9 ⇒ y = 4

Hence, the required number is, 10 × 4 + 9 = 49.

Step-by-step explanation:

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