Question

The ratio between a two digit number and the number obtained on reversing its digits
is 4: 7. If the difference between the digits of the number is 3, find the number.
Solution​

Answer 1

Answer:

The original number is 36.

Step-by-step explanation:

Let the number be (10x + y),

So, the number reversed will be (10y + x)

Now,

we are given,

(10x + y) : (10y + x) :: 4 : 7

We know that,

Product of extremes = Product of means

Thus,

7 × (10x + y) = 4 × (10y + x)

70x + 7y = 40y + 4x

70x - 4x + 7y - 40y = 0

66x - 33y = 0

33(2x - y) = 0

2x - y = 0/33

2x - y = 0 ----- 1

Now,

If we observe closely the original number is less than the reversed number because the ratio is 4 : 7

So,

The difference of the reversed number will be positive,

Thus,

y - x = 3 ---- 2

Adding eq.1 and eq.2 we get,

(2x - y) + (y - x) = 0 + 3

2x - y + y - x = 3

∴ x = 3

Now, putting x = 3 in eq.2 we get,

y - (3) = 3

y - 3 = 3

y = 3 + 3

y = 6

Thus,

The original number was 10(3) + (6)

= 30 + 6

= 36

Hence,

The original number was 36.

Hope it helped and you understood it........All the best