Question

The sum of the digits of a two digit number is 10. The number formed by interchanging the digits is 36 less than the original number. Find the original number.

NCERT CLASS VIII A ​

Answer 1

Answer:

hi !!

Step-by-step explanation:

Let x = units digit

y = ten's digit

The value of the number is x + 10y

The new value after reversing the digits is 10x + y

Equations:

x + y = 10 and

10x + y = x + 10y - 36 or 9x - 9y = -36 or x - y = -4

Add the 2 equations, the result is 2x = 6

so x = 3 and y = 7

The original number is 73.

hope this helps u !!!

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Answer 2

Answer:

Let the unit's digit be x

Ten's digit = 10 - x

$new \: number = 10 \times x + 10 - x = 10x + 10 - x = 9x + 10 \\ \\ number \: after \: interchanged \: = 10(10 - x) + x = 100 - 10x + x = 100 - 9x \\ \\ acq \\ \\ 9x + 10 = 100 - 9x - 36 \\ \\ 9x + 10 = 64 - 9x \\ \\ 9x + 9x = 64 -10 \\ \\ 18x = 54 \\ \\ x = 3$

Unit's digit = 3

Ten's digit = 10 - 3 = 7

Number = 73