Question

The sum of the digits of a 2-digit number is 7. If the digits are reversed, the new number increased by 3 equals
4 times the original number. Find the original number.​

Answer 1

Answer :- 16

Let the tens and units digit be x and y respectively.

According to the question,

• Case 1

⇒ Sum of the digits is 7

⇒ x + y = 7 ...(1)

• Case 2

⇒ If the digits are reversed and the number formed and multiplied by 3 will be equal to 4 times the original number

⇒ New number + 3 = 4 × Original number

Because, a two digit number is of them 10a + b where a and b are tens and units digit respectively.

∴ Original number = 10x + y

and, New number = 10y + x [ ∵ Digits are reversed ]

⇒ (10y + x) + 3 = 4(10x + y)

⇒ 10y + x + 3 = 40x + 4y

⇒ 39x - 6y = 3

⇒ 13x - 2y = 1 ...(2)

Multiply (1) by 13, we get

⇒ 13x + 13y = 91 ...(3)

Subtract (2) from (3)

⇒ 13x + 13y - (13x - 2y) = 91 - 1

⇒ 13y + 2y = 90

⇒ 15y = 90

⇒ y = 6

Substituting [y = 6] in (1), we get

⇒ x + 6 = 7

⇒ x = 7 - 6

⇒ x = 1

So, The Original number = 10x + y

⇒ 10×1 + 6

⇒ 16

Hence, The Original number is 16.

Answer 2

Answer:

16 is answer dear friend