Question

The sum of a two-digit number and the number obtained by reversing the order of digits is 99. If the digits differ by 3, find the number.​

Answer 1

Answer:

The number is either 36 or 63

Step-by-step explanation:

Let the digit at tens place be x and units place be y

The two digit number = 10x + y

On reversing the digits,

The number obtained = 10y + x

Their sum = 99

10x + y + 10y + x = 99

11x + 11y = 99

11(x + y) = 99

x + y = 99/11

x + y = 9 — (1)

It's also given, the digits differ by 3.

If digit at tens place is greater than digit at units place :

x – y = 3 — (2)

Add both the equations,

x + y + x – y = 9 + 3

2x = 12

x = 12/2

x = 6

Tens digit = 6

Units digit = 9 – 6 = 3

Therefore, the number is 63

If digit at units place is greater than digit at tens place :

y – x = 3 — (3)

Add equations (1) and (3),

x + y + y – x = 9 + 3

2y = 12

y = 12/2

y = 6

Units digit = 6

Tens digit = 9 – 6 = 3

Then, the number is 36

Answer 2

✫ Question Given :

• The sum of a two-digit number and the number obtained by reversing the order of digits is 99. If the digits differ by 3, find the number.

✫ Required Solution :

• ⇒ let the digits are x and y

• ⇒ a number xy then= 10x + y

★ Reversing the Expression

• ⇒ yx = 10y + x

✫ According to Question :

• ⇒ x - y = 3 _____eq(1)

• ⇒ 10x + y + 10y + x = 99 ____eq(2)

★ From eq 2 we get ,

• ⇒ 10x + y + 10y + x = 99

• ⇒ 11x + 11y = 99

• ⇒ x + y = 9 ____eq (3)

★ From eq (1) we get ,

✫ we have :

• ⇒ x - y = 3

• ⇒ x = 3 + y

★ Substituting value of x in eq (3)

• ⇒ x + y = 9

• ⇒ 3 + y + y = 9

• ⇒ 2y = 6

• ⇒ y = 3

★ Substituting value of y in eq(1)

• ⇒ x - y = 3

• ⇒ x - 3 = 3

• ⇒ x = 6

✰ So the number is 36 or 63 ✰

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