Question

1910.
Sum of the digits of a two-digit number is 8. The number obtained by interchanging
the digits exceeds the original number by 18. Find the number.​

Answer 1

✬ Original Number = 35 ✬

Step-by-step explanation:

Given:

• Sum of digits of two digit number is 8.
• After interchanging the digits the new number exceeds original by 18.

To Find:

• What is the number ?

Solution: Let tens digit be x and ones digit be y. Therefore

➨ Number = 10x + y and

➟ Tens + ones digit = 8

➟ x + y = 8

➟ x = 8 – y......(1)

[ Now interchanging digits new number formed will be ]

➙ Reversed number = 10y + x

A/q

• Reversed number exceeds original by 18.

$\implies{\rm }$ 10x + y + 18 = 10y + x

$\implies{\rm }$ 10x – x + 18 = 10y – y

$\implies{\rm }$ 9x + 18 = 9y

$\implies{\rm }$ 18 = 9y – 9x

$\implies{\rm }$ 2 = y – x

$\implies{\rm }$ 2 = y – (8 – y)

$\implies{\rm }$ 2 = y – 8 + y

$\implies{\rm }$ 2 + 8 = 2y

$\implies{\rm }$ 10 = 2y

$\implies{\rm }$ 5 = y

So, Digits of number are

➯ Ones place digit = y = 5

➯ Tens place digit = 8 – 5 = 3

Hence, the number is 10(3) + 5 = 35

Answer 2

$\large{\red{\underline{\underline{\bold{Given:-}}}}}$

• The sum of digits in a two digit number is 8.

• The number obtained by interchanging
the digits exceeds the original number by 18.

$\large{\blue{\underline{\underline{\bold{To\:Find:-}}}}}$

• The original number

$\large{\green{\underline{\underline{\bold{Solution:-}}}}}$

Let the digit at the ones place be x

Then digit at tens place = (8 - x)

The original number = 10(8 - x) + x

By interchanging the digits

The number obtained = 10x + (8 - x)

According to condition 2:-

$\rightarrow \sf \{10x + (8 - x )\} - \{10(8 - x) + x \} = 18$

$\rightarrow \sf (10x + 8 - x )- (80 - 10x+ x ) = 18$

$\rightarrow \sf (9x + 8 )- (80 - 9x ) = 18$

$\rightarrow \sf 9x + 8 - 80 + 9x = 18$

$\rightarrow \sf 18x - 72 = 18$

$\rightarrow \sf 18x = 18 + 72$

$\rightarrow \sf 18x = 90$

$\rightarrow \sf x = \dfrac{90}{18}$

$\rightarrow \sf x = 5$

Therefore:-

The ones digit of the number = x = 5

The tens digit of the number = 8-x = 8 - 5 = 3

Hence:-

$\large\boxed { \sf \purple{ \therefore The \: original \: number \: = 35}}$