A challenging question for you guys ....❤❤
solve it fast....
a two digit number is 4 times of its digit find the number also equal to 3 times the product of digit . find the number.
best one I will mark as brainiest...❣❣❣
Answers
Answer:24
Step-by-step explanation:
A two digit positive integer can be expressed as 10x+y
Where x is the tens digit and y is the ones digit
10x+y = 4(x+y)
10x+y = 3xy
10x+y = 4x+4y
10x - 4x = 4y -y
6x = 3y
y = 2x
Since y = 2x and 10x+y = 3xy
we have 10x+2x = 3x(2x) 12x =6x^2
6x^2-12x = 0
6x(x-2) = 0
x = 0 or x = 2
Since x can't be zero, x = 2
y = 2x = 4
The number is 24
Let the digit in the unit's place be y .
Let the digit in the ten's place be x.
The number is x y ( not x times y )
The two digit number can always be written in the form 10 x + y.
For example : 44 = 4×10 + 4
56 = 5×10 + 6
Given : The two digit number is 4 times the sum of the digits .
The two digit number is 10 x + y and sum of the digits is x + y
==> 10 x + y = 4 ( x + y )
==> 10 x + y = 4 x + 4 y
==> 6 x - 3 y = 0
==> 3 ( 2 x - y ) = 0
==> 2 x - y = 0
==> 2 x = y ................(1)
Also given : the number is 3 times the product of its digits :
The product of the digit is x y
==> 10 x + y = 3 x y
==> 10 x + 2 x = 3 x ( 2 x ) [See (1) ]
==> 12 x = 6 x²
==> 2 = x [ Cancelling 6 x both sides ]
==> x = 2
Now using (1) we can find the value of y.
==> y = 2 x
==> y = 2×2
==> y = 4
Remember our beautiful number was 10 x + y
==> 10 ×2 + 4
==> 20 + 4
==> 24
Hence the number is 24.
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