Question

Seven times a two digit number is
equal to four times the number
obtained by reversing the places of its
digits. If the difference between the
digits is 3, find the number.​

Answer 1

Answer:

Let tens digit be y and unit digit be x

So, we get :-

$\: \: \: \: \: \: \: \: \: \: \: 10y + x$

Reversed digit will be :-

$\: \: \: \: \: \: \: \: \: \: \: 10x + y$

● According to the question :-

$\: \: \: \: \: \: \: \: 7(10y + x) = 4(10x + y) \\ = > \: \: \: 70y + 7x = 40x + 4y \\ = > \: \: \: 70y - 4y = 40x - 7y \\ = > \: \: \: \: \: \: \: \: \: \: \: \: \: \: 66y = 33x \\ \\ we \: get \: x = 2y$

Now , it is given that :-

$\: \: \: \: \: \: \: \: \: \: x - y = 3$

From x = 2y :-

$\: \: \: \: \: \: \: \: \: \: 2y - y = 3 \\ = > \: \: \: \: \: \: \: \: \: \: \: \: y = 3$

So ,

$x = 2y = > 2 \times 3 \\ \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: = > 6$

✨ Required no. is 10y + x

=> 10 × 3 + 6

=> 36

Hope it helped ✌️ ✌️