Question

1) The digit in the tens place of a two-digit number is three times that in the ones
place. If the digits are reversed, the new number will be 36 less than the original
number. Find the number.
2) The numerator of a rational number is less than its denominator by 3. If the
numerator becomes three times and the denominator is increased by 20, the
new number becomes . Find the original number.​

Answer 1

Step-by-step explanation:

let the number be 10x + y

so according to condition 1

x=3y ___(1)

if digit are reversed then the number formed

10y +x

It is given that difference is 36

10x +y - (10y + x ) = 36

10x + y - 10y - x = 36

9x - 9y = 36

9(x - y) = 36

x - y = 4

3y - y = 4 ( from (1))

2y = 4

y = 2

then from (1)

x = 3y

x = 3 ×2

x = 6

so the original number was 10x + y

= 62

reverse it

26

and

62 - 26 = 36

Hence it is verified also