Question

10. A two-digit number is 4 more than 6 times the sum of its digits. If 18 is subtracted from the
number, the digits are reversed. Find the number.​

Answer 1

Answer:

Number = 64

Step-by-step explanation:

Given:

• A two digit number is 4 more than 6 times the sum of the digits
• If 18 is subtracted from the number, the digits are reversed

To Find:

• The number

Solution:

Let the unit's digit of the number be y.

Let the ten's digit of the number be x.

Hence,

The number = 10x + y

By given,

The number = 4 + 6 (sum of the digits)

10x + y = 4 + 6 (x + y)

10 x + y = 4 + 6x + 6y

4x = 4 + 5y

x = (4 + 5y )/4------(1)

Also by given,

Original number - 18 = Reversed number

Hence,

10x + y - 18 = 10y + x

Substitute the value of x from equation 1,

10 × (4 + 5y)/4 + y - 18 = 10y + (4 + 5y)/4

(40 + 50y)/4 + y - 18 = 10y + 1  + 5y/4

(40 + 50y)/4 + y = 10y + 19 + 5y/4

Multiplying whole equation by 4,

40 + 50y + 4y  = 40y + 76 + 5y

40 + 54y = 45y + 76

54y - 45y = 76 - 40

9y = 36

y = 4

Hence the units digit of the number is 4.

Substitute the value of y in equation 1,

x = (4 + 5 × 4)/4

x = 24/4

x = 6

Hence the ten's digit of the number is 6.

Therefore the number is 64.

Answer 2

Answer:

Given :-

• A two digits number is 4 more than 6 times the sum of its digits.
• 18 is substracted from the number, the digits are reserved.

To Find :-

• What is the number.

Solution :-

» Let, the two digits number be 10x + y

And, the reversed number will be 10y + x

➣ According to the question,

⇒ 10x + y = 6(x + y) + 4

⇒ 10x + y = 6x + 6y + 4

⇒ 10x - 6x + y - 6y = 4

⇒ 4x - 5y = 4 .... equation no (1)

➛ Now,we substracted 18 from the number 10x + y and the number will be reversed and we get,

⇒ 10x + y - 18 = 10y + x

⇒ 10x - x + y - 10y - 18 = 0

⇒ 9x - 9y = 18

⇒ x - y = 2 .... equation no (2)

➛ By multiplying the equation no (2) with 4 and from the equation no (1) we get,

⇒ 4x - 5y - 4x + 4y = 4 - 8

⇒ - y = - 4

⇒ y = 4

➛ By substituting y = 4 in the equation no (2) we get,

⇒ x - 4 = 2

⇒ x = 2 + 4

⇒ x = 6

➯ Hence, the required number is,

⇒ 10x + y

⇒ 10(6) + 4

⇒ 60 + 4

➠ 64

∴ The number is 64 .

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