Math, asked by noorfathima88, 5 months ago

10. Find three consecutive even numbers whose sum is 234.
11. The sum of the digits of a two-digit number is 12. If the new number formed by reversing
the digits is greater than the original number by 54, find the original number. Check your
solution.
12. The digit in the tens place of a two-digit number is three times that in the units place. If the
digits are reversed, the new number will be 36 less than the original number. Find the
original number. Check your solution.



plz solve this all questions very important if u give my answer so I mark answer brainlist plzz​

Answers

Answered by simran7539
12

10) ☆ Solution

Given :-

  • Sum is 234.

To Find :-

  • Three consecutive even numbers.

Step-by-Step-Explaination :-

Let the first even number be x

Then,

Second number = x + 2

Third number = x + 4

So,

x + x + 2 + x + 4 = 234

3x + 6 = 234

3x = 234 - 6

3x = 228

x = 228/3

x = 76

So,

Numbers are :-

First Number = x = 76

Second Number = x + 2 = 76 + 2 = 76

Third Number = x + 4 = 76 + 4 = 80

____________________________

11) ☆ Solution

Given :-

  • The sum of the digits of a two-digit number is 12. If the new number formed by reversing
  • the digits is greater than the original number by 54.

To Find :-

  • The original number

Step-by-Step-Explaination :-

Let the digit at unit place be x

Let the digit at tens place be 12 - x

Original Number = 10 ( 12 - x ) + 1 ( x )

= 120 - 10x + x

= 120 - 9x

New Number = 10 ( x ) + 1 ( 12 - x )

= 10x + 12 - x

= 9x + 12

According to the condition,

New number - Original number = 54

( 9x + 12 ) - ( 120 - 9x ) = 54

=> 9x + 12 - 120 + 9x = 54

=> 18x - 108 = 54

=> 18x = 54 + 108

=> 18x = 162

=> x = 162/18

=> 9

The Original Number = 120 - 9x = 120 - 9 (9)

= 120 - 81 = 39

Hence,

The original number = 39

Check -

1) According to the condition,

The sum of the digits of a two-digit number is 12.

The digit are 3 and 9

Thus,

Sum of 3 and 9 = 12

Checked

2) According to the condition,

The new number is greater than the original number by 54.

New number = 93

Original number = 39

93 > 39

93 - 39 = 54

Checked

____________________________

12) ☆ Solution

Given :-

  • The digit in the tens place of a two-digit number is three times that in the units place. If the digits are reversed, the new number will be 36 less than the original number .

To Find :-

  • The original number.

Step-by-Step-Explaination :-

Let the digit of unit place be x and tens place be y

The original number = 10y + x

The reversed number = 10x + y

According to the question,

=> y = 3x ...........................eq(1)

and

=> 10y + x - 36 = 10x + y

=> 10y - y + x - 10x = 36

=> 9y - 9x = 36

=> 9 ( y - x ) = 36

=> y - x = 36/9

=> y - x = 4

=> 3x - x = 4 ......... [from (1)]

=> 2x = 4

=> x = 4/2

=> x = 2

Putting the value of x in equation (1), we get :-

y = 3 ( 2 )

y = 6

Therefore,

The original number = ( 10y + x ) = [ 10 ( 6 ) + 2 ] = 60 + 2 = 62

Check :

10y + x - 36 = 10x + y

10(6) + 2 - 36 = 10(2) + 6

60 + 2 - 36 = 20 + 6

62 - 36 = 26

26 = 26

____________________________

Similar questions