Question

The sum of the digits of a two-digit number is 7. If the digits are reversed, the new
number increased by 3. equals 4 times the original number. Find the original number:
1​

Answer 1

Answer:

Here is your answer !

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Answer 2

Answer:

The original number is $16.$

Step-by-step explanation:

Given:

The sum of the digits of a two-digit number is $7$. If the digits are reversed, the new number increases by $3$. which equals $4$ times the original number.

To find the original number.

Step 1

Let the two-digit number be a and b

$10 a+b$

Given that $-a+b=7$

$a=7-b \quad.............(1)$

After reversing the digits,

New number $=10 b+a$

Step 2

According to the question:-

$10 b+a+3 &=4(10 a+b)$

Simplifying the above equation, we get

$10 b+a+3 &=40 a+4 b$

$10 b-4 b+3 &=40 a-a$

Step 3

Equating natural numbers,

$6 b+3 &=39 a$

$39 a-6 b &=3$

By substituting the value of $a$, then we get

$&39(7-b)-6 b=3$

$&273-39 b-6 b=3$

$&273-3=-(-39 b-6 b)$

Equating the above equation, we get

$270=45 b}$

$\frac{270}{45} =b$

$b=6}$

$&a=7-6$

$&a=1$

Step 4

Substitute the value of $a$ in the original equation, and we get

Original Number  $&=10 a+b$

$&=10(1)+6 \end{aligned}$

$&=10+6$

$=16$

Therefore, the original number is $16.$

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