The difference between a two-digit number and the number obtained by interchanging the digits is 36

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Click here👆to get an answer to your question ✍️ The difference between a two - digit number and the number obtained by interchanging the digits is 36. What is the difference between the sum and the difference of the digits of the number if the ratio between the digits of the number is 1 : 2 ?

Question

The difference between a two-digit number and the number obtained by interchanging the digits is 36. What is the difference between the sum and the difference of the digits of the number if the ratio between the digits of the number is 1 : 2 ?

A

4

B

8

C

16

D

None of these

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The difference between a two

The difference between a two-digit number and the number obtained by interchanging the digits is 36. What is the difference between the sum and the difference of the digits of the number if the ratio between the digits of the number is 1 : 2 ? a) 4 b) 8 c) 16 d) None of these

Examveda

The difference between a two-digit number and the number obtained by interchanging the digits is 36. What is the difference between the sum and the difference of the digits of the number if the ratio between the digits of the number is 1 : 2 ?

A. 4 B. 8 C. 16 D. None of these

Answer: Option B

Solution(By Examveda Team)

Since the number is greater than the number obtained on reversing the digits, so the ten's digit is greater than the unit's digit.

Let ten's and unit's digits be 2x and x respectively.

Then, (10 × 2x + x) - (10x + 2x) = 36

⇒ 9x = 36 ⇒ x = 4

∴ Required difference

= (2x + x) - (2x - x)

= 2x = 8

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Join The Discussion Comments ( 1 )

Apoorva Chatterjee :

2 years ago

Let X be the ten's digit and Y be the one's digit

(10X+Y)

The no formed can be interchanged which is

(10Y+X) Therefore,

(10X+Y) - (10Y+X) =36

X-Y=4

Required difference was

= (2x + x) - (2x - x)

= 2x = 8

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The difference between a two digit number and the number class 10 maths CBSE

The difference between a two digit number and the number obtained by interchanging the digits is 36 What is the difference between the sum and the difference of the digits of the number if the ratio between

The difference between a two digit number and the number obtained by interchanging the digits is 36. What is the difference between the sum and the difference of the digits of the number if the ratio between the digits of the number is 1 : 2?

(a) 4 (b) 8 (c) 16 (d) None of these Answer Verified 159.9k+ views 6 likes

Hint: Here, we need to find the difference between the sum and the difference of the digits of the number. Let the digit at ten’s place be

x x

and the digit at unit’s place be

y y

. A two-digit number can be written as 10

× ×

the digit at ten’s place

+ +

the digit at unit’s place. We will write the original and the reversed number in terms of

x x and y y

. Then, using the given information, we can form two linear equations in two variables. We will solve these equations to find the values of

x x and y y

, and thus, the original two digit number. Finally, we will use the digits to find the difference between the sum and the difference of the digits of the number.

Complete step-by-step answer:

We will use two variables

x x and y y

to form a linear equation in two variables using the given information.

A two-digit number can be written as 10

× ×

the digit at ten’s place

+ +

the digit at unit’s place.

For example, 28 can be written as

2×10+8 2×10+8 .

Let the digit at ten’s place be

x x

and the digit at the unit's place be

y y . Assume that x>y x>y .

Therefore, we get the first number as

10×x+y=10x+y 10×x+y=10x+y

When the digits are interchanged, the digit at ten’s place becomes

y y

and the digit at unit’s place becomes

x x .

We can write the number when the digits are interchanged as

10×y+x=10y+x 10×y+x=10y+x

Now, it is given that the difference between the two digit number and the number obtained by interchanging the digits is 36.

Thus, we get ⇒(10x+y)−(10y+x)=36 ⇒(10x+y)−(10y+x)=36

Simplifying the expression, we get

⇒10x+y−10y−x=36 ⇒10x+y−10y−x=36

Adding and subtracting the like terms, we get

⇒9x−9y=36 ⇒9x−9y=36

Factoring the number 9, we get

⇒9(x−y)=36 ⇒9(x−y)=36

Dividing both sides of the equation by 9, we get

⇒x−y=4………(1) ⇒x−y=4………(1)

It is given that the ratio of the digits of the two digit number is 1: 2.

Since x>y x>y , we get ⇒y:x=1:2 ⇒y:x=1:2

Rewriting the equation, we get

⇒ y x = 1 2 ⇒yx=12

Multiplying both sides of the equation by 2, we get

⇒2y=x ⇒2y=x

Rewriting the equation, we get

⇒x=2y………(2) ⇒x=2y………(2)

We can observe that the equations

(1) (1) and (2) (2)

are a pair of linear equations in two variables.

We will solve the equations to find the values of

x x and y y . Substituting x=2y x=2y in equation (1) (1) , we get ⇒2y−y=4 ⇒2y−y=4

Subtracting the like terms, we get

∴y=4 ∴y=4 Substituting y=4 y=4 in the equation x=2y x=2y , we get ⇒x=2(4) ⇒x=2(4)

Multiplying the terms in the expression, we get

∴x=8 ∴x=8

Therefore, we get the original two digit number as

10x+y=10(8)+4=80+4=84

10x+y=10(8)+4=80+4=84

Now, we will find the sum and difference of the digits.

Adding the digits of the number 84, we get

Sum of digits =8+4=12 =8+4=12

Subtracting the digits of the number 84, we get

Difference of digits

=8−4=4 =8−4=4

Finally, subtracting the difference of the digits from the sum of the digits, we get

Difference between the sum and the difference of the digits of the number

=12−4=8 =12−4=8

Therefore, we get the difference between the sum and the difference of the digits of the number as 8.

Thus, the correct option is option (b).Note: We have formed two linear equations in two variables and simplified them to find the number. A linear equation in two variables is an equation of the form

ax+by+c=0 ax+by+c=0 , where a a and b b

are not equal to 0. For example,

2x−7y=4 2x−7y=4

is a linear equation in two variables.

We can verify our answer by using the given information.

The number obtained by reversing the digits of 84 is 48.

We can observe that 84−48=36 84−48=36 .

Thus, the difference of the number and the number formed by interchanging the digits is 36.

The ratio of the digits 4 and 8 is 1: 2.

Hence, we have verified our answer.

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