Question

A two digit number is 7 times the sum of its two digits. the number that is formed by reversing its digits is 18 less than the original number. what is the number?

Answer 1

10x+y=7(x+y)
10x+y=7x+7y
3x=6y
X=2y

10y+x=10x+y-18
9y=9x-18
9Y=9x-18
Y=x-2
Y=2y-2
2=y

X=4

So number is 42 and 24

Answer 2

Solution :-

Let the digit at the ten's place be x ; and the digit at the unit's place be y.

Then,

The number will be = 10x + y.

A/Q, (1st condition)

$10x + y = 7(x + y) \\ \implies10x + y = 7x + 7y \\ \implies3x = 6y \\ \implies \: x = 2y \: \: \: \: \: ....(i)$

The number formed by reversing the digits is 10y + x.

A/Q, (2nd condition)

$10y + x = (10x + y) - 18 \\ \implies \: 10y - y = 10x - x - 18 \\ \implies \: 9y = 9x - 18 \\ \implies \: y = x - 2 \\ \implies y = 2y - 2 \: \: \: \: \: ...{using(i)} \\ \implies \: y = 2.$

From eq, (i)

x = 2 × 2 = 4.

Hence the required number is 42.