Question

4. 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?​

Answer 1

AnswEr:

Original Number is 26.

Step By Step Explanation:-

Let us Consider that one digit be x.

Then, other Digit be y.

$:\implies\sf\; y = 3x$

So, Original Number formed Will be

$:\implies\sf\; 10 \times \; x + 3x$

$:\implies\sf\; 10x + 3x$

$:\implies\large\boxed{\sf{\red{13x}}}$

$\bold{\underline{\sf{According\; to\; Question\; Now,}}}$

After Interchanging Digits, the Number Becomes

$:\implies\sf\; 3x \times\; 10 + x$

$:\implies\sf\; 30x + x$

$:\implies\large\boxed{\sf{\red{31x}}}$

$\rule{150}3$

$\bold{\underline{\sf{ Now,\; Adding\; both\; Numbers}}}$

$:\implies\sf\; 13x + 31x = 88$

$:\implies\sf\; 44x = 88$

$:\implies\sf\; \dfrac{88}{44}$

$:\implies\large{\underline{\boxed{\sf{\pink{x = 2}}}}}$

$\rule{150}3$

Now, Substituting the value of x.

$:\implies\sf\;x \times\; 10 + 3x$

$:\implies\sf\;2 \times \; 10 + 3(2)$

$:\implies\sf\;20 + 6$

$:\implies\large{\underline{\boxed{\sf{\pink{26}}}}}$

$\bold{\underline{\sf{Original\; Number\; is \; 26.}}}$

$\rule{150}3$

Answer 2

Answer:

Step-by-step explanation:

Given :-

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.

To Find :-

The Number

Solution :-

Let the digits at tens place be x.

And ones place be 3x .

Original Number = 10x + 3x = 13x

Number after interchanging = 10 × 3x + x = 30x + x = 31x

According to the Question,

⇒ Original number + New number = 88

⇒ 13x + 31x = 88

⇒ 44x = 88

⇒ x = 88/44

⇒ x = 2

Original Number = 13x = 13 × 2 = 26

Therefore, by considering the tens place and ones place as 3x and x.

The two digit number obtained is 62.

Hence, the two-digit number may be 26 or 62.