A quarter is one fourth of a dollar but Mr. Brainteaser has...........letter by a digit to make above solution correct ?

Question

A quarter is one fourth of a dollar but Mr. Brainteaser has changed the equation as below :

DOLLAR * 4 = QUARTER

Can you replace each letter by a digit to make above solution correct ?

Answer 1

To answer this we have to look at the multiples of 4 and it's patterns at its units place.
We can see that A and R are repeated on both sides

Now looking at R on both sides we can conclude that it is 0 because only when 4*0 we get 0 back and we have R at both side's units place.

We have 2 Ls on Dollar side and corresponding to those digits we have RT on other side.
Since we already found out what R is (0), to find L we just have to see what value of L will create a carry over that gives us 0 corresponding to R.
This found to be 7
ie., only when 77*4 = 308
Here 3 is irrelevant and all other numbers except 0 which is already taken gives some other value at R's place.
The last 3 digits on the Dollar side could be done by trial and error.
The answer is

457730( - DOLLAR ) ×4 = 1830920( - QUARTER)
D - 4
O - 5
L - 7
A - 3
R - 0
Q - 1
U - 8
T - 9
E - 2

Answer 2

457730 * 4 = 1830920
(DOLLAR * 4 = QUARTER)