Question

4
Q.13 A number consists of two digits whose sum is 12. If 18 is added to the number, the digits are reversed,
Find the number,​

Answer 1

Answer:

Step-by-step explLet us call a the tens digit and b the units digits. The permitted values for a are 1 to 9; for b, 0 to 9. The sum of the digits is

a + b = 12;

The requested number is therefore

N = 10a + b;

and the number formed by reversing the digits is

M = 10b + a.

If you add 18 to N, you get M, that is, in algebraic form:

N + 18 = M;

or, using the last expressions for N ad M,

10a + b + 18 = 10b + a;

by subtracting a and b from both terms, we get

10a +b + 18 – a – b = 10b + a – a – b;

9a + 18 = 9b;

and, by dividing both terms by 9, we get

a + 2 = b.

By replacing this value for b in the first equation, we get

a + b = a + a + 2 = 2a + 2 = 12

that is, by subtracting 2 from both terms,

2a = 10

or

a = 5;

b = a + 2 = 7.

The requested number is therefore

N = 57.

In fact, if you add 18 to it, you get 57 + 18 = 75, which has the same digits in reversed order.anation: