Question

On reversing the digits of a two digit number obtained is 9 less than three times the original number. If the difference of these two numbers is 45 find the original number​

Answer 1

original number: 27

reversed number: 72

Explanation:

Let the tens place digit = a

Let the units place digit = b

⇒ Original two-digit number = 10a + b

⇒ Reversed two-digit number = 10b + a

If the reversed two-digit number is 9 less than 3 times the original number:

⇒ 10b + a = 3(10a + b) - 9

⇒ 10b + a = 30a + 3b - 9

⇒ 7b = 29a - 9

If the different of the two numbers is 45 (and the reversed number is larger than the original number):

⇒ (10b + a) - (10a + b) = 45

⇒ 10b + a - 10a - b = 45

⇒ 9b -9a= 45

⇒ 9(b - a)= 45

⇒ b - a= 5

⇒ b = 5 + a

Substitute b = 5 + a into 7b = 29a - 9 and solve for a:

⇒ 7(5 + a) = 29a - 9

⇒ 35 + 7a = 29a - 9

⇒ 44 = 22a

⇒ a = 2

Finally, substitute the found value of a into b = 5 + a and solve for b:

⇒ b = 5 + 2 = 7

Therefore,

• original number: 27
• reversed number: 72