Question

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.

Answer 1

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

Answer 2

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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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