Question

One of the two digits of a two digit number is three times the other digit. If you
interchange the digits of this two-digit number and add the resulting number to the
original number, you get 88. What is the original number?
this is right ans or not​

Answer 1

Solution :-

Let the two digit number be xy where x is at tens place and y is at ones place

Therefore,

xy = 10x + y. ...eq( 1 )

Now,

According to the question,

y = 3x. ...eq( 2 )

Subsitute eq( 2 ) in eq( 1 ) , we get :-

= 10x + y

= 10x + 3x = 13x

Now,

By interchanging the digits we get,

yx = 10y + x. ...eq( 3 )

Subsitute eq( 3 ) in eq( 2 ) , we get :-

= 10y + x

= 10( 3x) + x

= 30x + x = 31x

Now,

According to the question,

Sum of original number and resulting number equal to 88

13x + 31x = 88

44x = 88

x = 88/44

x = 2

Thus, The value of x is 2

Subsitute the value of x in eq( 2 ) we get :-

y = 3x

y = 3 * 2 = 6

Hence, The original number will be 26$.$

Answer 2

QuestioN :

One of the two digits of a two digit number is three times the other digit. If you  interchange the digits of this two-digit number and add the resulting number to the  original number, you get 88. What is the original number?

GiveN :

• the two digits of a two digit number is three times the other digit.
• the resulting number to the  original number, you get 88.

To FiNd :

• The original number?

ANswer :

The original number is 26,62

SolutioN :

$\sf Let \:the\: digit\: in \:units\: place\: be\: x.$

$\sf Then,\: digit\: in\: ten's \:place =3x$

$\sf So, \:original\: number\: =10(3x)+x=31x$

$\sf On \:interchanging \:the\: digits, \:new\: number =10x+3x=13x$

$\sf According \:to\: the\: given\: condition,$

$\sf 31x+13x=88$

⇒$\sf 44x=88$

⇒$\sf x=2$

$\sf So, \:the\: original \:number\: is \:31x \:or \:31\:x\:2=62.$

On the other hand, if we consider the digit in ten's place as x, then the digit in unit's place will be 3x.

$\sf So, \:the\: resulting \:number\: we\: get\: is\: 26.$

$\sf \therefore\: Hence,\: The\: original \:number\: is\: 26,62.$

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