Question

the sum of the digits of a two digit number is 15 if the number formed by reversing the digit is less than the original number by 27 ​

Answer 1

Answer:

The number is 96.

Step-by-step explanation:

Solution :

Let the digits of Orignal Number be -

• Units place as y
• Tens place as 10(15 - y)

Digits reversed -

• Units place as 10(y)
• Tens place as (15 - y)

⇒ (10y + 15 - y) + 27 = 10(15 - y) + y

⇒ 9y + 15 + 27 = 150 - 10y + y

⇒ 9y + 42 = 150 - 9y

⇒ 9y + 9y = 150 - 42

⇒ 18y = 108

⇒ y = 108/18

⇒ y = 6

Units digit = 6

Tens digit -

⇒ 10(15 - 6)

⇒ 10(9)

⇒ 90

Orignal Number -

⇒ 90 + 6

⇒ 96

Therefore, the number is 96.

Answer 2

Answer:

96

Step-by-step explanation:

let the no. of the 2 digits be 10x+y

sum of the digits is 15

therefore,

x+y=15-----》1

no formed by reversing the digit =(10y+x)

(10x+y )-(10y+x)=27

9x - 9y = 27------》2

equation 2 dividing by 3

3x-3y=9------》3

again dividing it by 3

x-y=3------》4

solving by 1 and 4

x=9

y=6

the original no is 10x+y

=》10(9)+6

=》90+6

=》96