Question

The sum of the digits of a two-digit number is 7. If the digits are reversed , the new number increased by 3 less than 4 times the original number . Find the original number.​

Answer 1

Let the two digit number be, 10x + y.

So,

x + y = 7

x = 7 - y .... (i)

After reversing the digits, New number = 10y + x

According to the question :

10y + x + 3 = 4(10x + y)

10y + x + 3 = 40x + 4y

10y - 4y + 3 = 40x - x

6y + 3 = 39x

39x - 6y = 3

On, putting the value from (i), we get,

39(7 - y) - 6y = 3

273 - 39y - 6y = 3

273 - 3 = - (- 39y - 6y)

270 = 45y

y = 270/45

y = 6

So, x = 7 - 6 = 1

Original number = 10x + y = 10(1)+ 6 = 16