Math, asked by shubhamtomar, 1 year ago

Seven times a two digit number is equal to four times the number obtained by reversing the digits. If the difference between the digits is 3, find the number.

Answers

Answered by Hritika17
34
Let the digits be x and x+3
∴the number=10x+x+3
                     = 11x+3
reversed number=10x+30+x
                             =11x+30
By the problem,
7*(11x+3)=4*(11x+30)
⇒77x+21=44x+120
⇒33x=99
⇒x=3

∴The number is 36

nachiketathakur: how is the reversed number 11x + 30?
Hritika17: Reverse number will be=10(x+30)+x
nachiketathakur: ok
Answered by abcxyz12
12
\mathcal{\huge{\purple{\star\:Hayy \: Mate...!! \:\star}}}

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Let the ten's digits of the required number be x.

And, the unit's digit be y.

Then, the number = ( 10x + y ) .

The number obtained by reversing the digits = ( 10y + x ) .

A/Q,

•°• 7( 10x + y ) = 4( 10y + x ) .

=> 70x + 7y = 40y + 4x .

=> 70x - 4x = 40y - 7y .

=> 66x = 33y .

=> 66x - 33y = 0.

=> 33( 2x - y ) = 0.

=> 2x - y = 0.

•°• y = 2x............(1) .

▶ Now, sum of the digits is 3 .

=> x + y = 3 ...............(2) .

[ Putting the value of y ] .

=> x + 2x = 3 .

=> 3x = 3 .

=> x = 3/3 .

•°• x = 1 .

▶ On putting the value of x in equation (2), we get

=> 1 + y = 3 .

=> y = 3 - 1 .

•°• y = 2 .

Therefore, the required number = 10x + y .

= 10 × 1 + 2 .

= 10 + 2 .

✔✔ Hence, the required number is 12 ✅✅.

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