Answer

Verified

453.3k+ 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

Why Are Noble Gases NonReactive class 11 chemistry CBSE

Let X and Y be the sets of all positive divisors of class 11 maths CBSE

Let x and y be 2 real numbers which satisfy the equations class 11 maths CBSE

Let x 4log 2sqrt 9k 1 + 7 and y dfrac132log 2sqrt5 class 11 maths CBSE

Let x22ax+b20 and x22bx+a20 be two equations Then the class 11 maths CBSE

Trending doubts

Which are the Top 10 Largest Countries of the World?

Fill the blanks with the suitable prepositions 1 The class 9 english CBSE

Difference between Prokaryotic cell and Eukaryotic class 11 biology CBSE

Difference Between Plant Cell and Animal Cell

Give 10 examples for herbs , shrubs , climbers , creepers

Change the following sentences into negative and interrogative class 10 english CBSE

Differentiate between homogeneous and heterogeneous class 12 chemistry CBSE

The Equation xxx + 2 is Satisfied when x is Equal to Class 10 Maths

Fill the blanks with proper collective nouns 1 A of class 10 english CBSE