Question

A two digit number is four times the sum of the digits. If 36 is added to the number, the digits are reversed. Find the number ​

Answer 1

Answer :-

• The number is 28$.$

Given :-

• A two digit number is four times the sum of the digits.
• If 36 is added to the number, the digits are reversed.

To find :-

• The number.

Solution :-

Let assume the digit unit be x

Tenth place be y

ACCORDING TO QUESTION,

The number is 4 times the sum of 2 digits so ,

10y + x = 4(x + y)

10y + x = 4x + 4y

4x + 4y - 10y - x = 0

3x - 6y = 0

3(x - 2y) = 0

X - 2y = 0

So, x - 2y is first equation

NOW AFTER REVERSING the number so number formed is 10x + y.

Given that,

If 36 is added to the original number the digits are reversed so ,

(10y + x) + 36 = 10x + y

10x + y - 10y - x = 36

9x - 9y = 36

9(x - y) = 36

X - y = 36/9

X- y = 4

So, x - y = 4 is 2nd equation

Now we have to find the x and y value. so now,

Subtracting the eq 1 from equation 2

We get,

(X - y) - ( x - 4y) = 4 - 0

X - y - x + 4y = 4

Y = 4

Putting the value of y in eq 1 we get

X - 2 × 4 = 0

X - 8 = 0

X = 8

Hence, required number is 10 × 2 + 8 = 28

Verification :-

➝ 10y + x = 4(x + y)

➝ 10(4) + 8 = 4(8 + 4)

➝ 40 + 8 = 4(12)

➝ 48 = 48

LHS = RHS

Hence, Verified.

Answer 2

Given:-

.A two digit no. is four times the sum of the digits.

.If 36 is added to the number,the digits are reversed.

To Find:-

. The number =?

Solution:-

Let the digit unit be x.

Tenth place be y.

According to the question,

The number is 4 times the sum of 2 digits

so,

10y + x =4(x+y)

10y + x =4x +4y

4x + 4y -10y - x=0

3x -6y=0

3(x -2y)=0

x -2y=0

So,x -2y is first equation.

Now, after reversing the number so number formed is 10x + y.

Given that,

If 36 is added to the original number the digits are reversed so,

(10y + x) +36=10x +y

10x +y - 10y - x= 36

9x -9y = 36

9(x - y)=36

x - y=36/9

x -y=4

So, x -y = 4 is second equation.

Now,we have to find the x and y value.So now,

Subtracting the eq (1) from the eq (2)

(x - y)-(x + 2y)=4 -0

x - y - x - 2y = 4

Y = 4

Putting the value in eq (1)

x -2 × 4 =0

x - 8 =0

x =8

Hence,required number is 10 × 2 + 8 =28.