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.
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Answers
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