Question

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

Answer 1

Correct Question:

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

Answer:

The Original Number is 16.

Step-by-step explanation:

Given :

Sum of the Digits = 7

The new number = 3 less than 4 times the original number.

To Find :

The Original Number

Solution :

◆ $\textbf{\small{\underline{Consider the -}}}$

• Units Place as x
• Tens Place as 10(7 - x)

==> 10(7 - x) + x

==> 70 - 10x + x

==> 70 - 9x ...... [Original Number]

$\rule{300}{1.5}$

◆ $\textbf{\small{\underline{Number with Reversed Digits -}}}$

Consider the -

• Units Place as 10(x)
• Tens Place as (7 - x)

==> 10(x) + (7 - x)

==> 10x + 7 - x

==> 9x + 7 ...... [Reversed Digits]

$\rule{300}{1.5}$

◆ $\textbf{\small{\underline{According to the Question -}}}$

The new number = 3 less than 4 times the original number.

==> 9x + 7 = 4(70 - 9x) - 3

==> 9x + 7 = 280 - 36x - 3

==> 9x + 7 = - 36x + (280 - 3)

==> 9x + 7 = - 36x + 277

==> 9x + 36x = 277 - 7

==> 45x = 270

==> x = 270/45

==> x = 6

$\rule{300}{1.5}$

★ Value of (70 - 9x)

==> 70 - 9(6)

==> 70 - 54

==> 16

Original Number = 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

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

$\rule{300}{1.5}$

✯ According to the Question -

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

$\sf{\implies} \: 10b + a = 4(10a + b) - 3 \\ \sf{\implies} \:39a - 6b = 3 \\ \sf{\implies} \:13a - 2b =1 \:..(Equation \: 2)$

$\rule{300}{1.5}$

✯ Multiply Equation (1) by (2)

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

$\rule{300}{1.5}$

✯ 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 =

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

$\therefore$ The Original Number is 16.