A two-digit number is obtained by either multiplying the sum of the digits by 8 and then subtracting 7or by multiplying the difference of the digits by 18and then adding 1. Find the number. [Assume thatten's digit is greater than units digit.]

A two-digit number is obtained by either multiplying the sum of the

1.	A two-digit number is obtained by either multiplying the sum of the digits by 8 and then subtracting 7or by multiplying the difference of the digits by 18and then adding 1. Find the number. [Assume thatten's digit is greater than units digit.]
Answer» tenth's digit be x and one's digit be y.Then the NUMBER is 10x+y. By the first condition-(x+y)×8−5=10x+y⇒2x−7y=−5 ........(i) By the SECOND condition-(x−y)×16+3=10x+y⇒6x−17y=−3 ..........(II)Multiplying (i) by 3, we get6x−21y=−15 .......(iii)SUBTRACTING (ii) from (iii), we get−4y=−12⇒y=3. Substituting y=3 in (i)2x−7×3=−5⇒x=8 ∴ The number is 10×8+3=83.Hope it helps