Question

the sum of two digit number is 15. number 9btained by interchanging its digits exceed the given number by 9. find the number ​

Answer 1

✬ Number = 78 ✬

Step-by-step explanation:

Given:

• The sum of two digit number is 15.
• Number obtained by interchanging its digit exceed the given number by 9

To Find:

• What is number?

Solution: Let the digit at ones place be y and digit at tens place be x.

• Number = 10x + y

Sum is of digits of the number is 15

• x + y = 15 .......(1)

Number obtained by interchanging digits will be 10y + x.

A/q

$\small\implies{\sf }$ 10y + x = 10x + y + 9

$\small\implies{\sf }$ 10x – x + y – 10y = –9

$\small\implies{\sf }$ 9x – 9y = –9

$\small\implies{\sf }$ 9 (x – y) = –9

$\small\implies{\sf }$ x – y = –1......(2)

• Solving equations 1 and 2 •

$x + y = 15 \\ x - y = - 1 \\ \\ 2x = 14 \\ \\ = > x = \frac{14}{2} \\ \\ = > x = 7$

Put the value of x in equation 1

$\small\implies{\sf }$ x + y = 15

$\small\implies{\sf }$ 7 + y = 15

$\small\implies{\sf }$ y = 8

∴ Number = 10x + y

→ 10(7) + 8

→ 70 + 8

→ 78

Answer 2

Step-by-step explanation:

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