Question

The result of dividing a two digit number by the number formed by reversing the digits is 25/19. the difference between the two digits is 2. find the two digit number

Answer 1

Answer :

Let the two digit number be 10x + y.

Then, the number formed by reversing the digits will be 10y + x.

According to the question,

$\frac{10x + y}{10y + x} = \frac{25}{19}$

Thus,

$→19(10x + y) = 25(10y + x) \\ \\ →190x + 19y = 250y + 25x \\\\→ 190x - 25x = 250y - 19y \\ \\ →165x = 231y \\ \\→ x = \frac{231y}{165} .................eq1$

And,

Difference between the two digits = 2

Hence, x - y = 2 .................... eq2

Now,

Using eq1 in eq2, we get

$→x - y = 2 \\\\ →\frac{231y}{165} - y = 2 \\\\ → \frac{231y - 165y}{165} = 2 \\\\ → \frac{66y}{165} = 2 \\ \\→ y = \frac{2 \times 165}{66} = 5$

Hence, if y = 5 then x = y+2 = 7.

Therefore, the two digit number is 75.