Question

the sum of the digits of a two number is 10. The number formed by reversing the digits is 18 less than the original number. Find the original number.​

Answer 1

Answer:

The Original Number is 64.

Step-by-step explanation:

Given :

Sum of the digits = 10

Number formed after reversing the digits = 18 less than the original number

To find :

The Original Number

Solution :

Original Number -

Let the digits be =

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

$\longrightarrow$ 10(10 - x) + x

$\longrightarrow$ 100 - 10x + x

$\longrightarrow$ 100 - 9x ...... [Original Number]

$\rule{300}{1.5}$

Number with Reversed Digits -

Let the digits be =

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

$\longrightarrow$ 10(x) + (10 - x)

$\longrightarrow$ 10x + 10 - x

$\longrightarrow$ 9x + 10 ....... [Number With Reversed Digits]

$\rule{300}{1.5}$

According to the Question -

Number having reversed digits = 18 less than original Number

$\longrightarrow$ 9x + 10 = (100 - 9x) - 18

$\longrightarrow$ 9x + 10 = 82 - 9x

$\longrightarrow$ 9x + 9x = 82 - 10

$\longrightarrow$ 18x = 72

$\longrightarrow$ x = 72/18

$\longrightarrow$ x = 4

$\rule{300}{1.5}$

★ Original Number -

$\longrightarrow$ 100 - 9(4)

$\longrightarrow$ 100 - 36

$\longrightarrow$ 64

$\therefore$ The Original Number is 64.