Question

The tens digit of a two digit number is five more than the units digit. Seven times the sum of the digits of this number is 3 less than the number itself. Find the number.

Answer 1

94

Explanation:

Let the unit's digit =
`y`

Let the ten's digit =
`x`

Then the number will be equal to
`10x+y`

Now, using the given statement:

`x=y+5 ..... (1)`

`7(x+y) = 10x+y-3\\\Rightarrow 7x+7y=10x+y-3\\\Rightarrow 6y-3x=-3 ..... (2)`

Now, using the equation (1) in equation (2):

`6y-3(y+5) =-3\\\Rightarrow 3y-12=0\\\Rightarrow y =4`

By equation (1):

`x = 4+5 \\\Rightarrow x =9`

Therefore, the number is :

`10x+y= 10* 9 +4 = \bold{94}`