Question

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.​

Answer 1

Answer:

842

Step-by-step explanation:

let the digits be x, y, z. the number if x y z

given,

x=4*z -------1

x+y+z =14 --------2

100*x+10*y+z=100*z+10*y+x+594---------3

by simplifying 3

x - z=6

from 1

4z - z = 6

z=2

then x=8 , y=4

Answer 2

Answer:

842

Step-by-step explanation:

Let’s consider the digit at tens place as x

And let the digit at unit place be y

Then, the digit at hundred place = 4y

Hence, the number is 100 x 4y + 10 × x + y × 1 = 400y + 10x + y = 401y + 10x

So, reversing the number = 100 × y + 10 × x + 4y × 1 = 100y + 10x + 4y = 104y + 10x

Then according to the first condition given in the problem, we have

x + y + 4y = 14

x + 5y = 14 … (i)

And according to the second condition given in the problem, we have

401y + 10x = 104y + 10x + 594

401y – 104y = 594

297y = 594

y = 594/297

y = 2

On substituting the value of y in equation (i), we have

x + 5(2) = 14

x + 10 = 14

x = 14 – 10

x = 4

Therefore, the number is = 10x + 401y = 10(4) + 401(2) = 40 + 802 = 842.