eight times a two digit number is equal to 3 times the number obtained by reversing the order of the digits if the difference between the digits of the number is 5 find the number
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Answered by
9
THANKS FOR THE QUESTION !
_____________________________
GIVEN :
=> 8 TIMES A 2 DIGIT NO. IS EQUAL TO 3 TIMES THE NO. OBTAINED BY REVERSING ITS DIGITS
_____________________________
LET,
THE DIGIT AT THE UNIT PLACE OF THAT NO.
=> X
THE DIGIT AT THE TENSE PLACE OF THAT NO.
=> Y
______________________________
SEE :
HOW A NO. IS MADE :
=> SUPPOSE 45
=> 4 * 10 + 5
MEANS ,
=> TENSE DIGIT * 10 + UNITS DIGIT
______________________________
THEN OUR NO. :
=> TENSE DIGIT * 10 + UNIT'S DIGIT
=> Y * 10 + X
=> 10Y + X
______________________________
AND IF THE DIGITS ARE INTERCHANGED ,
=> THE NEW NO. :
=> UNIT'S DIGIT * 10 + TENSE DIGIT
=> 10 * X + Y
=> 10X + Y
______________________________
FROM THE GIVEN CONDITION ,
=> 8 ( 10Y + X ) = 3 ( 10X + Y )
=> 80Y + 8X = 30X + 3Y
=> 80Y - 3Y = 30X - 8X
=> 77Y = 22 X
=> 77Y - 22X = 0
=> 22X - 77Y = 0
______________________________
THE DIFFERENCE BETWEEN THE TWO DIGITS IS GIVEN :
=> 5
_____________________________
FROM THIS INFO,
=> UNIT'S DIGIT - TENSE DIGIT = 5
=> X - Y = 5
=> MULTIPLY THIS EQUATION BY 27
=> 22X - 22Y = 5 ( 22 )
=> 22X - 22Y = 110
______________________________
SUBSTRACT THE TWO EQUATIONS ,
=> 22X - 77Y = 0
=> 22X - 22Y = 110
=> WE WILL GET,
=> - 55Y = - 110
=> Y = -110 / -55
=> Y = 2
_____________________________
PUT Y = 2 IN THIS EQUATION TO GET X ,
=> X - Y = 5
=> X - 2 = 5
=> X = 5 + 2
=> X = 7
_____________________________
ORIGINAL NO.
=> 10 * Y + X
=> 10 * 2 + 7
=> 20 + 7
=> 27
_____________________________
HOPE IT WILL HELP U ......
THANKS AGAIN .....
_____________________________
_____________________________
GIVEN :
=> 8 TIMES A 2 DIGIT NO. IS EQUAL TO 3 TIMES THE NO. OBTAINED BY REVERSING ITS DIGITS
_____________________________
LET,
THE DIGIT AT THE UNIT PLACE OF THAT NO.
=> X
THE DIGIT AT THE TENSE PLACE OF THAT NO.
=> Y
______________________________
SEE :
HOW A NO. IS MADE :
=> SUPPOSE 45
=> 4 * 10 + 5
MEANS ,
=> TENSE DIGIT * 10 + UNITS DIGIT
______________________________
THEN OUR NO. :
=> TENSE DIGIT * 10 + UNIT'S DIGIT
=> Y * 10 + X
=> 10Y + X
______________________________
AND IF THE DIGITS ARE INTERCHANGED ,
=> THE NEW NO. :
=> UNIT'S DIGIT * 10 + TENSE DIGIT
=> 10 * X + Y
=> 10X + Y
______________________________
FROM THE GIVEN CONDITION ,
=> 8 ( 10Y + X ) = 3 ( 10X + Y )
=> 80Y + 8X = 30X + 3Y
=> 80Y - 3Y = 30X - 8X
=> 77Y = 22 X
=> 77Y - 22X = 0
=> 22X - 77Y = 0
______________________________
THE DIFFERENCE BETWEEN THE TWO DIGITS IS GIVEN :
=> 5
_____________________________
FROM THIS INFO,
=> UNIT'S DIGIT - TENSE DIGIT = 5
=> X - Y = 5
=> MULTIPLY THIS EQUATION BY 27
=> 22X - 22Y = 5 ( 22 )
=> 22X - 22Y = 110
______________________________
SUBSTRACT THE TWO EQUATIONS ,
=> 22X - 77Y = 0
=> 22X - 22Y = 110
=> WE WILL GET,
=> - 55Y = - 110
=> Y = -110 / -55
=> Y = 2
_____________________________
PUT Y = 2 IN THIS EQUATION TO GET X ,
=> X - Y = 5
=> X - 2 = 5
=> X = 5 + 2
=> X = 7
_____________________________
ORIGINAL NO.
=> 10 * Y + X
=> 10 * 2 + 7
=> 20 + 7
=> 27
_____________________________
HOPE IT WILL HELP U ......
THANKS AGAIN .....
_____________________________
Krishnamrita:
ya
according to equation that will also change
according to the taking .....
of x and y and their places .... I think I have clearified ur doubts.... is it ok now
why we should subtract tens digit from ones digit not ones digit from tens digit
why x-y not y-x. Plz clear the doubt
for the clearification plz kindly do the sum taking the different variables
u will automatically understand it
and for ur understanding ..... I had done it from both the ways but it didn't give ans.... because in the question the condition is not mentioned clearly means whether tense is greater than units or units is greater than tense ..... so i had done it in both ways but 2nd way wasn't of use thus I gave this way ....
clear ?
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Answer:27
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