Question

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

Answer 1

Answer :-

The original number is 16.

Solution :-

Let the digits of the two digit number be x and y

Sum of the digits of a two digit number = 7

⇒ x + y = 7

⇒ x = 7 - x --(1)

Original number = 10x + y

New number when digits are reversed = 10y + x

According to the question

⇒ 10y + x = 4(10x + y) - 3

⇒ 10y + x = 40x + 4y - 3

⇒ 3 = 40x + 4y - 10y - x

⇒ 3 = 39x - 6y

⇒ 3 = 3(13x - 2y)

⇒ 3/3 = 13x - 2y

⇒ 1 = 13x - 2y ---(2)

Substitute (1) in (2)

⇒ 1 = 13(7 - y) - 2y

⇒ 1 = 91 - 13y - 2y

⇒ 1 = 91 - 15y

⇒ 15y = 91 - 1

⇒ 15y = 90

⇒ y = 90/15

⇒ y = 6

Substitute y = 6 in (1)

⇒ x = 7 - y

⇒ x = 7 - 6

⇒ x = 1

Original number = 10x + y = 10(1) + 6 = 10 + 6 = 16

Therefore the original number is 16.

Answer 2

Answer:

The Original Number is 16.

Step-by-step explanation:

Gívєn -

Sum of the Digits = 7

The Number with Reversed Digits is 3 less than the 4 times of Original Number

Tσ fínd -

The Original Number

Sσlutíσn -

Let the digits be -

• Units Place = a
• Tens Place = b

The original number = 10a + b

Sum of digits--> 7

$\sf{\implies} \: a + b = 7 \: ......(1)$

$\rule{300}{1.5}$

According to the Question -

The Number with Reversed Digits is 3 less than the 4 times of Original Number

$\sf{\implies} \: 10b + a = 4(10a + b) - 3$

$\sf{\implies} \: 39a - 6b = 3$

$\sf{\implies} \: 13a - 2b = 1 \: .......(2)$

$\rule{300}{1.5}$

Multiply Equation (1) by (2)

$\sf{\implies} \:2a + 2b = 14 \: ......(3)$

$\rule{300}{1.5}$

Add the Equation (2) and (3)

$\sf{\implies} \:15a = 5$

$\sf{\implies} \:a = 1 \\ \sf{\implies} \:b = 6$

$\rule{300}{1.5}$

The Original Number =

$\sf{\implies} \:10a + b = 10(1) + 6 \\ \sf{\implies} \:16$

$\therefore$ The Original Number is 16.