Question

*1)* A two digit number is 3 more than 4 times the sum of its digits. If 18 is added to this

number, the sum is equal to the number obtained by interchanging the digits. Find the

number.​

Answer 1

Answer:

Let the digit in ten's place be x and the digit in one's place be y.

The original no. = 10x+y

A/q

Case I

$\: \: \: \: \: \: \: \: 10x + y = 4(x + y) + 3 \\ = > 10x + y = 4 x + 4y + 3 \\ = > 6x - 3y = 3 \\ = > 2x - y = 1$

______________________(i)

Case II

$\: \: \: \: \: \: \: 10x + y + 18 = 10y + x \\ = > 9x - 9y = - 18 \\ = > x - y = - 2$

_______________________(ii)

Now,

(i) - (ii)

$\: \: \: \: \: \: \: 2x - y - x + y = 1 + 2 \\ = > x = 3$

Therefore,

y = 3+2 [from (ii) ]

= 5

Hence, the digit is 35.