The sum of the digits of a twodigit number is 12. If the new number fo – InterviewSolution

1.

The sum of the digits of a twodigit number is 12. If the new number formed by reversing thedigits is greater than the orignal number by 54,find the orignalnumber.I hope someone would answer it as quickly they can.Pls don't answer this question more points, if you know then only answer it. Thnxs

Answer»

Given :

The SUM of the digits of a two digit number is 12.
When the digits are interchanged the new number formed is greater than original number by 54.

To Find :

The original number

Solution :

Let the digit at the tens PLACE be X.

Let the digit at the units place be y.

Original Number = (10x+y)

Case 1 :

The sum of digits at the tens place and units place is 12.

$\implies$ $\sf{x+y=12}$

$\sf{x=12-y\:\:\:\:\:(1)}$

Case 2 :

The digits when interchanged of the original number, the new number formed is greater than original number by 54.

Reversed Number = (10y+x)

Equation :

$\implies$ $\sf{10y+x=10x+y+54}$

$\implies$ $\sf{10y-y=10x-x+54}$

$\implies$ $\sf{9y=9x+54}$

$\implies$ $\sf{9y=9(12-y) +54}$

$\implies$ $\sf{9y=108-9y+54}$

$\implies$ $\sf{9y+9y=108+54}$

$\implies$ $\sf{18y=162}$

$\implies$ $\sf{y=\dfrac{162}{18}}$

$\implies$ $\sf{y=9}$

Substitute, y = 9 in equation (1),

$\implies$ $\sf{x=12-y}$

$\implies$ $\sf{x=12-9}$

$\implies$ $\sf{x=3}$

$\large{\boxed{\bold{Ten's\:digit\:=\:x\:=\:3}}}$

$\large{\boxed{\bold{Unit's\:digit\:=\:y\:=\:9}}}$

$\large{\boxed{\bold{\red{Original\:Number\:=\:10x+y=10(3)+9=30+9=39}}}}$

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