PLEASE HELP ME FRIENDS A number of three digits has the hundred digit 4 times the unit digit and the sum of three digits is 14. If the three digits are written in the reverse order ,the value of the number is decreased by 594. Find the number .
Answers
Let the -
- hundred's digit be x.
- ten's digit be y.
- one's digit be z.
A number of three digits has the hundred digit 4 times the unit digit.
=> x = 4z ___ (eq 1)
Also, sum of three digits is 14.
=> x + y + z = 14
Substitute value of x = 4z above
=> 4z + y + z = 14
=> 5z + y = 14 ___ (eq 2)
If the three digits are written in the reverse order ,the value of the number is decreased by 594.
Now,
Original number = 100x + 10y + z
=> 100(4z) + 10y + z
=> 400z + 10y + z
=> 401z + 10y
Reversed number = 100z + 10y + x
=> 100z + 10y + 4z
=> 104z + 10y
According to question,
=> 401z + 10y - (104z + 10y) = 594
=> 401z + 10y - 104z - 10y = 594
=> 297z = 594
=> z = 2
Hundred's digit = x
Substitute value of z in (eq 1)
=> x = 4(2)
=> x = 8
Ten's digit = y
Substitute value of z in (eq 2)
=> 5(2) + y = 14
=> 10 + y = 14
=> y = 4
One's digit = z
=> z = 2
We have to find the number.
So,
Number = 100x + 10y + z
=> 100(8) + 10(4) + 2
=> 800 + 40 + 2
=> 842
•°• Number is 842.
Step-by-step explanation:
Hola !
Let the unit digit has x
And let the ten digit has y
Such that,
X=4×y
Then the number is 4z+y+z=14,
5z+y=14
We had to take the number in order of digits .Such that
100x+10y+z
400z+10y+z
401z+10y->1
If it is reversed .Then it will be
100z+10y+4z
104z+10y->2
From equation 1&2 and the difference between them is 594
401z+10y-104z-10y=594
294z=594
z=2