Question

A 2-digit number us 3 more than 4 times the sum of its digits. If 18 is added to the number, it's digits are reversed. Find the number?

Answer 1

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Answer 2

ANSWER:-

Given:

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

To find:

Find the number.

Solution:

Let tens place digit be R and the units place be M.

Therefore,

Our number is (10R + M).

Given,

first condition is that our number is 3 more than 4 times the sum of its digits.

So,

According to the question:

=) 4(R+M) +3 =(10R + M)

=) 4R + 4M +3 = 10R +M

=) 4R -10R +4M-M = -3

=) -6R + 3M = -3

=) -2R + M = -1.............(1)

Second condition is that if 18 is added to the number, its digit are reversed.

So,

The reversed number is (10M +R).

Therefore,

=) (10R +M) +18 =10M + R

=) 10R - R +M -10M= -18

=) 9R - 9M = -18

=) 9(R- M) = -18

=) R - M= -18/9

=) R - M= -2..............(2)

Now,

Solving equation (1) & (2), we get;

=) -R = -3

=) R= 3

Putting the value of R in equation (1), we get;

=) -2(3) + M = -1

=) -6 + M= -1

=) M= -1+ 6

=) M= 5

So,

Our number is (10×3 +5)

=) 30+5

=) 35

Hence,

The number is 35.

Hope it helps ☺️