Question

The tens digit of a three-digit number is twice the
units digit. The hundreds digit of the number is twice
the tens digit. The number formed by reversing the
digits of the number is 594 less than it. The number
is​

Answer 1

Solution :-

Let us assume that, unit digit, tens digit and hundreds digits of the three digit number are x, y and z .

Than,

→ original number = (100*z + 10*y + x)

Given that,

→ tens digit = 2 * unit digit

→ y = 2x ------ Eqn(1)

and,

→ hundred digit = 2 * ten digit

→ z = 2y ------- Eqn(2)

Putting Eqn(1) in Eqn(2),

→ z = 2*(2x)

→ z = 4x

So,

→ Three digit number = (100*z + 10*y + x) = (100*4x + 10*2x + x) = 400x + 20x + x = 421x

Now,

→ When we reverse the digit, New number formed will be = (100*x + 10*y + z) = (100*x + 10*2x + 4x) = 100x + 20x + 4x = 124x .

we have given that, The number formed by reversing the

digits of the number is 594 less than original number .

Therefore,

→ 421x - 124x = 594

→ 297x = 594

→ x = 2 .

So,

→ y = 2x = 2*2 = 4

→ z = 4x = 4*2 = 8

Hence,

→ Original number = (100*z + 10*y + x) = 100*8 + 10*4 + 2 = 800 + 40 + 2 = 842 (Ans.)