Question

ek a two digit number is 3 more than 4 times the sum of it's digits if 18 is added to the number , its digits are reversed find the number​

Answer 1

Answer:

The no. is 35

Step-by-step explanation:

Let the number in units place be x

let te number in tens digit be y

Then the no. is (10y+x)

ATQ,

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

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

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

6y-3x=3

2y-x=1 .......(I)

IF 18 is added to the no. then it is reversed

ATQ,

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

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

9y-9x=-18

9x-9y=18

x-y = 18 .......(II)

On solving equation (I) and (II)

we get

y=3 ,

x=5

Hence the no. formed is (3×10+5)= 35.

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Answer 2

Since we have given that

Let the unit digit be 'x'.

And let the ten's digit be 'y'.

So, the two digit number will be 10y+x

According to question,

(10y + x) –4 (x + y) = 3

10y + x –4x –4y = 3

6y – 3x = 3

2y – x = 3 -------- [ 1 ]

If 18 is added to the number, the digit are reversed.

So, it becomes,

18 + 10y + x = 10x + y

18 = 10x - x + y - 10y

18 = 9x - 9y

2 = x - y -------- [ 2 ]

From eq(1) and (2), we get that

2y - x = 1

– y +x = 2

---------------------

y = 3

and x - y = 2

x - 3 = 2

x = 2 + 3

x = 5

So, the number will be

10y + x

= 10 × 3 + 5

= 30 + 5

= 35

Hence, the number will be 35.