Question

QUES : -The sum of the digits of a two digit number is 14. If 18 is subtracted from the number, digits are reversed. Find the number ? (A) 86 (B) 77 (C) 68 (D) 76

Answer 1

Answer:

• The number will be 86

Hence, option (A) 86 is correct.

Explanation:

Let,

• the unit digit of number be y

• and its tens digit be x

• and the number will be 10 x + y

then,

sum of digits is 14

→ x + y = 14  

→ x = 14 - y    ____equation (1)

and,

On reversing the digits number formed will be 10 y + x

so,

on subtracting 18 from the number digits will be reversed

→ 10 x + y - 18 = 10 y + x

→ 9 x - 9 y - 18 = 0

→ x - y - 2 = 0

[ using equation (1) ]

→ 14 - y - y - 2 = 0

→ 14 - 2 y - 2 = 0

→ - 2 y + 12 = 0

→ y = 6

[ putting value of y in equation (1) ]

→ x = 14 - 6

→ x = 8

therefore,

• The number is 10 x + y = 10 ( 8 ) + 6 = 86 .

Answer 2

Answer:

(A) 86

The number is  86

Step-by-step explanation:

Let,

The units digit = x

The tens digit = 14 - x

★ Orignal Number :

⇒ 10 (14 - x) + x

⇒ 140 - 10x + x

⇒ 140 - 9x

★ Digit of the number reversed :

⇒ 10x + (14 - x)

⇒ 10x - x + 14

⇒ 9x + 14

★According to the question:

⇒ (140 - 9x) - 18 = 9x + 14

⇒ 140 - 9x - 18 = 9x + 14

⇒ 140 - 18 - 9x = 9x + 14

⇒ 122 - 9x = 9x + 14

⇒ - 9x - 9x = 14 - 122

⇒ - 18x = - 108

⇒ 18x = 108

⇒ x = 108 / 18

⇒ x = 6

★ The unit digit = 6

The tens digit = 14 - x

⇒ 14 - x

⇒ 14 - 6

⇒ 8

★ The tens digit = 8

Therefore,

(A) 86

The number is  86