Question

the ratio of tens digit to one's digit of a number is 2:3 .if 27 is added to the number the digits interchange their places.find the number​

Answer 1

Answer:

The number is 69

Step-by-step explanation:

Let the number be 10m + n

where m is the digit in tens place and n is the digit in ones place.

So, reversing it we will get,

10n + m

Now, we are given,

m : n = 2 : 3

So,

Let m = 2x and n = 3x

Then,

The number becomes,

10(2x) + (3x)

= 20x + 3x

= 23x

Then,

The reversed number becomes,

10n + m

= 10(3x) + (2x)

= 30x + 2x

= 32x

Now, according to the Question,

Number + 27 = Number reversed

23x + 27 = 32x

Solving for x,

32x - 23x = 27

9x = 27

x = 27/9

x = 3

Hence,

m = 2x = 2(3) = 6

n = 3x = 3(3) = 9

So,

The original number becomes,

10m + n = 10(6) + (9)

= 60 + 9

= 69

Hence,

The number is 69.

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