A two digit number is obtained by multiplying the sum of digits by 8

2 digit number is obtained by either multiplying the sum of the digits by 8 and subtracting 5 or by multiplying the difference of the digits by 16 and then adding so that two digit number is obtained by the two methods that we can multiply the sum of the digits by 8 and then we can subtract 5 or we can multiply the difference of the digits by 16 and then add three we have to find the number now let's suppose let X be the ones digit and Y be the tens digit me know that it is a two digit number it will have one sentence digits that supports this is once this is tense this is exit this is why

we know that if let's suppose we have a let's suppose we have to well that is a two digit numbers we are to write in terms of one sentence does it so we can write as as this is to is once again right 2 into 1 + as this is tense so 1 into 10 is equal to 1 into 10 10 + 2 that is 12 so basically will write our two digit as in the form of X and Y so we can write this as as as the ones digit into 1 + Y is 10 so why into 10 to write this as 10 Y + now according to the given condition the digit is equal to multiplying the sum of the digits by 8 and subtracting 5 so 10 Y + x is equal to multiplying the sum of the digits by its digits are x and y x + Y is multiplied

it and then this is subtracted by 5 so let's suppose this is the given conditions will solve this 10 Y + x is equal to 8 x + 8 Y - 5 so we can write this as let's suppose taking this term 2 lesson this is Rs so 8 x + 8 Y - 3 Y - x is equal to 5 now we can write this as a text message is 7 x 81 minus 3 Y is equal to minus 2 Y is equal to 5 this will be our first equation now the second condition is if multiplying the difference of the digits by 16 and then adding 3 sunao 10 vi

+ x is equal to multiplying difference of the digits by 16 16 16 into Y minus x + then adding 3 + 3 address as 10 Y + x is equal to 16 Y - 16 X + 3 taking this terms is Bhutan 12 will write this as 10 Y - 16 Y + X + 16 X is equal to 310 Y - 3 Y is this will be 17 x minus 6 Y is equal to 3 so this will be our second equation now we have two variables and two equations will solve this these two equations these are 7 x minus 2 Y 7 x minus 2

is equal to 5 and 7 3 x minus 6 Y is equal to 3 Sawal solve this equation first of all I will multiply will multiply this equation by multiplying this by because we multiply it by 3 this will get 6 vi and will cancel out this is it will be very easy for solving the soul 7 things that is 21 x minus 6 Y is equal to 35 years of 15 and 17 x minus 6 Y is equal to 3 Sona will subtract this two equations so this will be minus minus plus this will be -21 2017 will be 4 this will be cancel is equal to 15 - 3 that is 12 so this will be 4 x is equal to 12 equal to know the value of

x is equal to 3 no will find the value of y by putting the situation in putting the value of x in equation first so 7 x minus 2 Y + 7 x minus 2 Y is equal to 5 will put the value of x which will be 7 into 3 - 2 Y is equal to 5 7321 minus 2 Y is equal to 5 so now we can write this as 21 minus 5 is equal to minus 2 Y or minus 2 Y + + 2 Y is equal to 16 or we can say that the value of Y is equal to 8 week of the value of Y we got the value of x so we can write the digits that is why was the tenth place X was the one place showing red the two digit number is equal to 83

this will be our answer thank you

Answer

Verified

Hint: Firstly we have to assume the tens and ones term in the problem as x and y, so the number will be 10x+y. Then after reading the question we have to create the first equation by multiplying the sum of the digits by 8. Then after reading the second part we have to multiply the difference of the digits by 14 and add 2 with them. By doing this we can create a second equation. After getting two equations we have to just solve them so that we can get the number.

Complete step by step solution:
Let us assume that the tens digit is x and ones digit is y.
Then we get that the original number will be \[10x+y\].
According to the question the two digit number is obtained by multiplying the sum of the digit by 8.
So, we can write in mathematical form as below,
\[\begin{align}
  & 10x+y=\left( x+y \right)\times 8 \\
 & \Rightarrow 10x+y=8x+8y \\
 & \Rightarrow 2x-7y=0..............................\left( i \right) \\
\end{align}\]
We marked this equation as “i”.
In the question it is also said that the number is obtained by multiplying the difference of the digits by 14 and adding 2 in it.
Now, again we can express mathematically and we have the below equation,
\[\begin{align}
  & 10x+y=\left( x-y \right)\times 14+2 \\
 & \Rightarrow 10x+y=14x-14y+2 \\
 & \Rightarrow 4x-15y+2=0...............................\left( ii \right) \\
\end{align}\]
We marked this equation as “ii”.
By multiply equation “i” with 2 and subtract “ii” from it, we get,
\[\begin{align}
  & \left( 4x-14y \right)-\left( 4x-15y+2 \right)=0 \\
 & \Rightarrow 4x-14y-4x+15y-2=0 \\
 & \Rightarrow y-2=0 \\
 & \Rightarrow y=2 \\
\end{align}\]
Putting the value of \[y=2\] on equation “i” we get,
\[\begin{align}
  & 2x-7y=0 \\
 & \Rightarrow 2x-7\times 2=0 \\
 & \Rightarrow 2x=14 \\
 & \Rightarrow x=7 \\
\end{align}\]

In the beginning of this problem we assume the original number will be \[10x+y\]. Now after getting the value of \[x=7\] and \[y=2\]. We simply put these values to get the required number.
The number will be,
\[\begin{align}
  & 10x+y \\
 & \Rightarrow 10\times 7+2 \\
 & \Rightarrow 72 \\
\end{align}\]

Note: For calculating the equation we can take another route. In this problem we did this by multiplying equation “i” with 2 and subtracting it from “ii” to get the required value. We can simply evaluate equation “i” a little bit to get the value of 2x.
\[\begin{align}
  & 2x-7y=0 \\
 & \Rightarrow 2x=7y...................\left( iii \right) \\
\end{align}\]
And put the value of x in equation on “ii” and get,
\[\begin{align}
  & 4x-15y+2=0 \\
 & \Rightarrow 2\times 2x-15y+2=0 \\
 & \Rightarrow 2\times 7y-15y+2=0 \\
 & \Rightarrow -y+2=0 \\
 & \Rightarrow y=2 \\
\end{align}\]
And put the value of y in “iii” we get,
\[\begin{align}
  & 2x=7y \\
 & \Rightarrow 2x=7\times 2 \\
 & \Rightarrow x=7 \\
\end{align}\]
By this method we can solve this problem also.

Is a 2 digit number the sum of whose digits is 8?

What is a two

How many two

Are two