Question

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In a two-digit number the tens digit is four less than the units digit. Seven times the tens digit plus five times the units digit is equal to 56. Find the digits.

Answer 1

The digits are 37 (Thirty seven).

Explanation:

Given:

Two digit number.

Let the unit place digit be y

and

The tens place digit be (y - 4) as it is 4 less than the unit digit.

So the two digit number is (y-4)(y).

According to question:

Seven times the tens digit plus five times the units digit is equal to 56.

⇒
`7(y-4)+5(y)=56`

⇒
`7y-28+5y=56`

⇒
`12y=56+28` ... both sides subtarcting with 28

⇒
`12y=84`

⇒
`y=(84)/(12)=7, as\ 12*7=84` ...both sides dividing with 12

So the ones place digit is
`y=7` and tens place digit is
`(y-4)=(7-4)=3`

The number can be arranged as, from right side we have to put the unit digit and then the tens place digit.

So the digits are 37 in arranged order fulfilling our criteria.