Answer
Verified
482.1k+ views
Hint: Assume the number at one’s place, ten’s place. Then use the given conditions to write equations in two variables and solve them to find the number.
Let the digit in one’s place be \[x\] and ten’s place be \[{\text{ }}y\].
Original number is \[10y + x\].
Number formed by reversing the digits is \[{\text{ }}10x + y\]
Given that the number is ${\text{3}}$ more than ${\text{4 }}$ times the sum of its digits
\[ \Rightarrow 10y + x = 4(x + y) + 3\]
\[ \Rightarrow 10y + x - 4x - 4y = 3\]
\[ \Rightarrow 6y - 3x = 3\]
\[ \Rightarrow 2y - x = 1{\text{ }}...{\text{(1)}}\]
Also given that when \[{\text{18}}\] is added to the number the digits get interchanged.
Therefore, \[(10y + x) + 18 = {\text{ }}10x + y\]
\[ \Rightarrow 9x - 9y = 18\]
\[ \Rightarrow x - y = 2{\text{ }}...{\text{(2)}}\]
To find the values of\[{\text{ }}x\] and \[y\] ,add \[{\text{(1)}}\] and \[{\text{(2)}}\] , we get
\[ \Rightarrow 2y - y - x + x = 1 + 2\]
\[ \Rightarrow y = 3\]
Put\[y = 3\] in \[x - y = 2\], we get
\[ \Rightarrow x - 3 = 2\]
\[ \Rightarrow {\text{ }}x = 5\]
As we know,
The original number is \[{\text{(}}10y + x{\text{)}}\].
\[ \Rightarrow (10y + x) = 10(3) + 5 = 35{\text{ }}\]
Putting the values of\[x\]and \[y\] in original number, we get,
Hence, the number is \[{\text{35}}\].
Note: To solve such types of questions, all the conditions must be considered carefully and then equated. Also, the numbers at one's place and ten’s place must not be mixed.
Let the digit in one’s place be \[x\] and ten’s place be \[{\text{ }}y\].
Original number is \[10y + x\].
Number formed by reversing the digits is \[{\text{ }}10x + y\]
Given that the number is ${\text{3}}$ more than ${\text{4 }}$ times the sum of its digits
\[ \Rightarrow 10y + x = 4(x + y) + 3\]
\[ \Rightarrow 10y + x - 4x - 4y = 3\]
\[ \Rightarrow 6y - 3x = 3\]
\[ \Rightarrow 2y - x = 1{\text{ }}...{\text{(1)}}\]
Also given that when \[{\text{18}}\] is added to the number the digits get interchanged.
Therefore, \[(10y + x) + 18 = {\text{ }}10x + y\]
\[ \Rightarrow 9x - 9y = 18\]
\[ \Rightarrow x - y = 2{\text{ }}...{\text{(2)}}\]
To find the values of\[{\text{ }}x\] and \[y\] ,add \[{\text{(1)}}\] and \[{\text{(2)}}\] , we get
\[ \Rightarrow 2y - y - x + x = 1 + 2\]
\[ \Rightarrow y = 3\]
Put\[y = 3\] in \[x - y = 2\], we get
\[ \Rightarrow x - 3 = 2\]
\[ \Rightarrow {\text{ }}x = 5\]
As we know,
The original number is \[{\text{(}}10y + x{\text{)}}\].
\[ \Rightarrow (10y + x) = 10(3) + 5 = 35{\text{ }}\]
Putting the values of\[x\]and \[y\] in original number, we get,
Hence, the number is \[{\text{35}}\].
Note: To solve such types of questions, all the conditions must be considered carefully and then equated. Also, the numbers at one's place and ten’s place must not be mixed.
Recently Updated Pages
How many sigma and pi bonds are present in HCequiv class 11 chemistry CBSE
Mark and label the given geoinformation on the outline class 11 social science CBSE
When people say No pun intended what does that mea class 8 english CBSE
Name the states which share their boundary with Indias class 9 social science CBSE
Give an account of the Northern Plains of India class 9 social science CBSE
Change the following sentences into negative and interrogative class 10 english CBSE
Trending doubts
Fill the blanks with the suitable prepositions 1 The class 9 english CBSE
Which are the Top 10 Largest Countries of the World?
Give 10 examples for herbs , shrubs , climbers , creepers
Difference Between Plant Cell and Animal Cell
Difference between Prokaryotic cell and Eukaryotic class 11 biology CBSE
The Equation xxx + 2 is Satisfied when x is Equal to Class 10 Maths
Change the following sentences into negative and interrogative class 10 english CBSE
How do you graph the function fx 4x class 9 maths CBSE
Write a letter to the principal requesting him to grant class 10 english CBSE