Question

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Sum of the digits of a two-digit number is 9. When we interchange the digits, it is
found that the resulting new number is greater than the original number by 27. What
is the two-digit number? Solve,
4 One of the two digits of a two digit number is three times the other digit. If you​

Answer 1

Step-by-step explanation:

The sum of the digits of a two-digit number is 9. When we interchange the digits, it is found that the resulting new number is greater than the original number by 27. What is the two-digit number?

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There is a simple test for divisibility by 9 that states a number is divisible by 9 if (and only if) the (repeated) digit sum of the number is divisible by 9. For example, 18 and 81 are divisible by 9 because 1+8=9.

So the two-digit number we are looking for is divisible by 9.

Moreover the difference to another number divisible by 9 is 27. For the majority of numbers (those ending in 4 and higher), adding 27 lowers the units place by 3 so I started thinking about those, and quickly found 36. But a more structured way is nothing that the two-digit multiples of nine pair up:

18 <=> 81

27 <=> 72

36 <=

Productivity maximized.

Let the unit digit be y and tens digit be x

Number formed = 10x + y

Reverse number = 10y + x

x + y = 9 (Given)…………………………eq1

10y + x = 10x + y + 27…………………….eq2

9y - 9x = 27

y - x = 3……………………………………..eq3

Solving eq1 and eq3 ,we get

x = 3 and y = 6

Original Number = 36 Reversed Number = 63

You can crosscheck the answer by putting up the values obtained either in eq1 or eq2 or eq 3

Answer 2

Answer:

36

Step-by-step explanation:

Let units digit be x

and tens digit be y

According to question,

x+y=9   .....(1)

Also, given

10y+x=10x+y+27

=>9x-9y-27=0

=>y-x=3   ....(2)

Adding (1) and (2), we get

2y=12

=>y=6

=>x=9-y=9-6=3

So, the original number=10x+y=30+6=

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