Question

a two digit number is 3more than 4 times the sum of its digits. if 18 is added to the number,its digit are reversed.find the nunber
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Answer 1

Answer:

no.is 35

Step-by-step explanation:

Let the two digits of two digit number be y at 10s place and x at 1s place. Accordingly the number will be 10y + x

A two digit number is 3 more than 4 times the sum of its digits.

The sum of digits is x + y

(10y + x) = 4 ( y + x) + 3

10y + x = 4y + 4x + 3

10y - 4y + x - 4x = 3

6y - 3x = 3. .

2y - x = 1

2y = 1 + x .Eq..1

If 18 is added to the number, its digits are reversed. What is the number

(10y + x) + 18 = (10x + y)

10y + x + 18 = 10x + y

10y - y + x - 10x = - 18

9y - 9x = - 18

9 (y - x) = - 18

y - x = - 2

y = x - 2…Eq..2

Now derived value of y is substituted in Eq..1

2y = 1 + x

2(x - 2) = 1 + x

2x - 4 = 1 + x

2x - x = 1 + 4

x = 5

The 1s digit is 5

Substituting the value of x in Eq..2 to drive the value of y

y = x - 2

y = 5 - 2

y = 3

The digit at 10s place is 3, and at Is place is 5 therefore the number is 35.

Answer the number is 35

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