Question

A two digit number is 3 more than 4 times the sum of its digits. If 18 is added to the number, its digits are reversed. Find the number

Answer 1

Answer:35

Solution:-

Let the tens place be x and unit place be y

Now two digit no. is 3 more than 4 times the sum if its digits

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

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

10x-6x+y-4y=3

4x-3y=3

2x-y=1 .........i)

If 18 added to the no. its digits are reversed

10x+y+18=10y+x

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

9x-9y=-18

x-y=-2 .........ii)

On subtracting ii)from i)

x-y-2x-y=-2-1

-x-y-2x-y=-2-1

-x=-3

x=3

Now

2x-y=1

2×3-y=1

6-y=1

-y=-5

y=5

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Then the number=10x+y =10×3+5

=35

Answer 2

Given That:-

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

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

Assumption:-

Let the tens place of the digit be a and the ones place be b

Solution:-

Tens Place = 10 × a = 10a

Ones Place = b

We Know that,

Two digit number is 3 more than 4 times the sum of its digits, So-

10a + b = 4(a+b) + 3

10a + b = 4a + 4b +3

10 + b - 4a - 4b = 3

10a - 4a + b - 4b = 3

6a - 3b = 3

3(2a-b) = 3

2a - b = 3/3

2a - b = 1 (equation i)

Now, It is given that if 18 is added to the number, its digits are reversed, so-

10a + b + 18 = 10b + a

10a - a + b - 10b = -18

9a - 9b = -18

9(a-b) = -18

a-b = -18/9

a-b = -2 (equation ii)

Now, On subtracting equation i from equation ii we get,

(a-b) - (2a-b) = -2-1

a - 2a - b + b = -3

-a = - 3

a = 3

Now, the value of b is,

a-b = -2

3-b = -2

-b = -2-3

-b = -5

b = 5

Hence, the original digit is =10a+b = 10×3+5 = 30+5 = 35