Answer
425.1k+ views
Hint: Let the ones digit of the original number be x and the tens digit of the original number be y. So, the original number is 10y+x. So, use the statement that the two digit number is 3 more than 4 times the sum of its digits to form the first equation. When the digits are reversed the number we get is 10x+y which is equal to 18 added to the original number which will give the second equation. Solve the equations to get the answer.
Complete step-by-step answer:
Let the ones digit of the original number be x and the tens digit of the original number be y. So, the original number is 10y+x.
Now, it is given that the two digit number is 3 more than 4 times the sum of its digits, so if we represent this mathematically, we get
$ 10y+x=3+4\left( x+y \right) $
$ \Rightarrow 10y+x=3+4x+4y $
$ \Rightarrow 6y-3x=3.............(i) $
It is also given that when the digits are reversed the number we get is 10x+y which is equal to 18 added to the original number. So, if we represent this as an equation, we get
$ 10y+x+18=10x+y $
$ 9x-9y=18...........(ii) $
Now, we will multiply equation (i) by 3 and add it with equation (ii). On doing so, we get
$ 9x-9y-3\left( 6y-3x \right)=18-3\times 3 $
\[\Rightarrow -9y+18y=18+9\]
\[\Rightarrow y=\dfrac{27}{9}=3\]
If we substitute y in equation (i), we get
$ 6y-3x=3 $
$ \Rightarrow 6\times 3-3x=3 $
$ \Rightarrow 18-3=3x $
$ \Rightarrow x=\dfrac{15}{3}=5 $
Hence, the original number is 10y+x=30+5=35.
Note: Don’t get confused and consider the original to be yx, where y is a digit and x is another digit, because this will mean that the number is equal to the product of y and x while the number is actually equal to (10y+x). Also, make sure that you are not confused about which variable is the unit digit of the original number and which is the unit digit of the reversed number, as it might be very confusing.
Complete step-by-step answer:
Let the ones digit of the original number be x and the tens digit of the original number be y. So, the original number is 10y+x.
Now, it is given that the two digit number is 3 more than 4 times the sum of its digits, so if we represent this mathematically, we get
$ 10y+x=3+4\left( x+y \right) $
$ \Rightarrow 10y+x=3+4x+4y $
$ \Rightarrow 6y-3x=3.............(i) $
It is also given that when the digits are reversed the number we get is 10x+y which is equal to 18 added to the original number. So, if we represent this as an equation, we get
$ 10y+x+18=10x+y $
$ 9x-9y=18...........(ii) $
Now, we will multiply equation (i) by 3 and add it with equation (ii). On doing so, we get
$ 9x-9y-3\left( 6y-3x \right)=18-3\times 3 $
\[\Rightarrow -9y+18y=18+9\]
\[\Rightarrow y=\dfrac{27}{9}=3\]
If we substitute y in equation (i), we get
$ 6y-3x=3 $
$ \Rightarrow 6\times 3-3x=3 $
$ \Rightarrow 18-3=3x $
$ \Rightarrow x=\dfrac{15}{3}=5 $
Hence, the original number is 10y+x=30+5=35.
Note: Don’t get confused and consider the original to be yx, where y is a digit and x is another digit, because this will mean that the number is equal to the product of y and x while the number is actually equal to (10y+x). Also, make sure that you are not confused about which variable is the unit digit of the original number and which is the unit digit of the reversed number, as it might be very confusing.
Recently Updated Pages
How many sigma and pi bonds are present in HCequiv class 11 chemistry CBSE
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
Why Are Noble Gases NonReactive class 11 chemistry CBSE
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
Let X and Y be the sets of all positive divisors of class 11 maths CBSE
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
Let x and y be 2 real numbers which satisfy the equations class 11 maths CBSE
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
Let x 4log 2sqrt 9k 1 + 7 and y dfrac132log 2sqrt5 class 11 maths CBSE
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
Let x22ax+b20 and x22bx+a20 be two equations Then the class 11 maths CBSE
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
Trending doubts
Fill the blanks with the suitable prepositions 1 The class 9 english CBSE
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
At which age domestication of animals started A Neolithic class 11 social science CBSE
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
Which are the Top 10 Largest Countries of the World?
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
Give 10 examples for herbs , shrubs , climbers , creepers
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
Difference between Prokaryotic cell and Eukaryotic class 11 biology CBSE
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
Difference Between Plant Cell and Animal Cell
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
Write a letter to the principal requesting him to grant class 10 english CBSE
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
Change the following sentences into negative and interrogative class 10 english CBSE
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
Fill in the blanks A 1 lakh ten thousand B 1 million class 9 maths CBSE
![arrow-right](/cdn/images/seo-templates/arrow-right.png)