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
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
∴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?
Answered by
12
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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