What change occur if we interchange the digits in a number?

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?(a). 88(b). 26(c). 62(d). 68

Answer

Hint: First we will take the two digits number as xy and then we will apply the given condition in the question and then we will interchange the two digit number and it becomes yx and then we will add it to get our final answer of 88.Complete step-by-step solution -

Let the two digit number be xy.
Now as per the given question one of the two digits of a two digit number is three times the other digit.
Therefore,
y = 3x
Now we will break xy in tens and ones,
$xy=10x+y$
Now using y = 3x in the above equation we get our number as,
$\begin{align}
  & 10x+3x \\
 & =13x \\
\end{align}$
Now interchanging the digits of this two digit number we get
$yx=10y+x$
Now using y = 3x in the above equation we get our number as,
$\begin{align}
  & 10(3x)+x \\
 & =31x \\
\end{align}$
Now as per the question,
$\begin{align}
  & 31x+13x=88 \\
 & 44x=88 \\
 & x=\dfrac{88}{44} \\
 & x=2 \\
\end{align}$
Now putting the value of x in y = 3x we get,
y = $3\times 2$ = 6
Now the number that we took was xy and hence 26.
So, option (b) is correct.
And if we would have taken x = 3y then the answer that we get is 62.
So, option (c) is also correct.

Note: One thing in this question should be kept in mind that there are two answers to this question, so one might think after solving that only one answer is correct and can make mistakes so this should be kept in mind.

Jump to

• Exercise 2.1
• Exercise 2.2
• Exercise 2.3
• Exercise 2.4
• Exercise 2.5
• Exercise 2.6

• Rational Numbers
• Linear Equations in One Variable
• Understanding Quadrilaterals
• Practical Geometry
• Data Handling
• Squares and Square Roots
• Cubes and Cube Roots
• Comparing Quantities
• Algebraic Expressions and Identities
• Visualising Solid Shapes
• Mensuration
• Exponents and Powers
• Direct and Inverse Proportions
• Factorisation
• Introduction to Graphs
• Playing with Numbers

NCERT Solutions Class 8 Mathematics Solutions for Exercise 2.4 in Chapter 2 - Linear Equations in One Variable

Q4) 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:

Solution:

Let the unit place digit of a two-digit number be x.

Therefore, the tens place digit = 3x.

\because 2-digit number = 10 x tens place digit + unit place digit

\therefore Original number = 10\times3x+x=30x+x=31x

According to the question, New number + Original number = 88

\Rightarrow10x+3x+31x=88

\Rightarrow\ 44x=88

\Rightarrow\ x=\ \frac{88}{44}=2

Hence, the 2-digit number = 31x=31\times2=62.

Video transcript

"In this video we're going to solve this particular problem with States. One of the two digits of a Nugent number is 3 times the other digital if you interchange the digits of this budget number and there is a and add the resulting number to the original number you get 88. What is the original number? So he's kind of a word problem set to be really confusing at first. So let's break them down and we'll step as so let's go on to the first part over here that says one of the two digits over two digit number is 3 times the other side. So two digit number has in its place and hence least like one of the two digits is 3 times the other types of text appearance this as X. So the other one is 3 times x now in something it is very very important to multiply your densities within that something that you might tend to forget. For example, let's take a number 46, right? So it's very clear that I know the unit's case is 6 and the in space is for but it's not for actually into 1040 and then you have six and when you add the two you actually get the number. 36 just keep that in mind when deciding what was like so the Dead Space 2 x n so this becomes 10 into 3x. I think it's based X wanted that remains as it is and I have a senior 14 plastic to find a number would be 10 into 3 X Plus X. Now. This is what the problems are with X we can for the solo 2 this becomes 30 X Plus X and this becomes 31 x. So the number of we know is 31 x we're not on location will go happy the question and see if you interchange the digits of this two-digit number. Okay, so I'm going to Interchange that it is so on. Interchanging What do I get? You can space to store your ex will become now 3x and density is 2/3 x will become X. Like I said, the tens place will be multiplied by 10 which means by 1. So this is an X and 3X. The final number I have here is 10 x + 3 x again, we have x dot Senate at them and you get that as 14 x. Okay, so I have one number that you would is number and when I have are interchanging with it is negative 14x. Let's go back to questions. You got it right there as well. If you eat the change the digits of the two digit number and add the resulting number for the audition number add this resulting number. To the original Apple that is 31 x what will you get you get 88? So what you have are your is nothing but your equation working x + 31 x is equal to 88 13x plus 31 x is nothing but 44 x is equal to 88 any value of x so X is 88 of 144. I get x equal to now I have x equal to what would be the number I'll have to put the value of x in this equation. Right? So 21 x the number is equal to 31 x 50 1 into X is 2 Get 62, but number is 60. That's all in this video. Feel free to like comment and share and we get up you have any doubts even with no connection, and we will try our best to get back to you. That's all in this video. Thank you, and I'll see you next week"

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