LEW
ZHA
------------------
WXLE
ZWHA
XAXR
-------------
ZEWXWE
-------------

THIS ONE IS CORRECT. we can find solution

First check for the hints.i.e, X+1=Z and L+A=W these are the only hints we have.

in question,,, (1)LEW*Z=XAXR (2)LEW*H=ZWHA (3)LEW*A=WXLE

Among the three, select anyone to solve this puzzle.
Let us take eq (1) why becoz it contains all the letters of the hints L.A.W.X.Z as it becomes somewhat easy to solve.

1. start by taking X=1 and Z=2 then take W values other than the values of X and Z as like
W=2,3,4,5,6,7,8,9

2. by taking X=1,Z=2 and W=3,4,5,6,7,8,9 the eq.1 is not satiesfied for all values of W.
3. by taking X=2,Z=3 and W=1,4,5,6,7,8,9 the eq.1 is not satiesfied for all values of W.
4. by taking X=3,Z=4 and W=1,2,5,6,7,8,9 the eq.1 is not satiesfied for all values of W.
5. by taking X=4,Z=5 and W=1,2,3,6,7,8,9 the eq.1 is not satiesfied for all values of W.
6. by taking X=5,Z=6 and W=1,2,3,4,7,8,9 the eq.1 is not satiesfied for all values of W.

7. by taking X=6,Z=7 and W=1,2,3,4,5,7,8,9 LET US CHECK
8. put W=1 then LE1*7=6A67.we cannot get 6 at units place in 7th table and also there is no carry.

9.put W=2 then LE2*7=6A64 CARRY=1. 7*E must have 5 in its units place to get 6.only one is
7*5=35
put E=5 then L52*7=6A64 CARRY=3. 7*L must have 6 in its tens place . only one is 7*9=63
put L=9 then 952*7=6664.here, X and A are getting same values.so, it is not satisfying

10.put W=3 then LE3*7=6A61 CARRY=2. 7*E must have 4 in its units place to get 6.only possible one
for E is 2
put E=2 then L23*7=6A61 CARRY=1. 7*L must have 6 in its tens place.it is 7*9=63
put L=9 then 923*7=6461 it is satisfied
it also satisfies L+A=W ==> 9+4=3(carry=1)

11.check for eq.2 LEW*H=ZWHA
923*H=73H4 ==> H must be 8 to get 4 in units place of eq2
923*8=7384 ==> it is satisfied

12.check for eq.3 LEW*A=WXLE
923*4=3692 ==> it is satisfied

HENCE WE GOT THE SOLUTION!!!

923
784
------------
3692
7384
6461
------------
723632
------------

CHECT IT OUT..........!!!!

Break the qustion into Sub-Questions
We can proceed like this by taking these two multiplication simultaneously 1) L E W * A = W X L E 2) L E W * H = Z W H A
we will continue by hit and trial method
take eq 1)
start by taking the value of W as 2 as W cant be 1( as it is given L + A = W and neither A nor L can BE zero at any cost)
now keeping the value of A as 3 we will see that L E W * A = W X L E satisfy with these values 862 * 3 = 2586
but on the other hand if we put the respective value in eq 1) it fails 862 * H = Z2H3 as the last digit of result contain 3 which is only possible with 7*9 but here we are multiplying H*2.
now change the value of A as 4 5 6 7 8 9 u can easily find out in no time that none of the combiantion satisfy the eq 1)

now we will replace W with 3 and A with 4 ( because 2 is not a possible value for A as W is 3 and no number multiplied with 2 can give the leftmost digit of resultant as 3)
and this value will easily satisfy both the equation 1) 923 * 4 = 3692 and 2) 923 * 8 = 7384

now put the respective value in the given question and u can easily get all the digit value in one go.

L E W
Z H A
-------------
W X L E
Z W H A
X A X R
-------------
Z E W X W E


9 2 3
7 8 4
-------------
3 6 9 2
7 3 8 4
6 4 6 1
-------------
7 2 3 6 3 2

Hope it helps

I think the question is like this

LEW
* ZHA
--------------------
WXLE
ZWHA
XAXR
--------------
ZEWRXE
--------------

DANISH IQBAL@ I corrected it. you can check it !!

i didnt remember correctly. if any body knows xact, than correct it..... sorry for inconvinience

@SHAIK RUMANA I dont think this question is correct

But according to given question the result is ZEWRXE

LEW
ZHA
------------------
WXLE
ZWHA
XAXR
-------------
ZEWXWE
-------------

Here Note Few points

1) X + 1 = Z

2 ) W+X+1/2 = 10

In eq 2 Carry cannot be 2 Because in previous column X + H + R = X

that means H + R = X carry cannot be more than 1

S0

W +X =9

Possible values are
W X
1 8
2 7
3 6
4 5
5 4
6 3
7 2
8 1

W cannot be 0, 1 ,2 Check Other cases 3 and 6 in first attempt you will get answer

S0 w = 3 then X =6 that leads to z=7

All solutions given below is wrong... please veryfy crefuly...... and request to all... please submit correct question.... and give solution after cross cheaking... bina cheak kiye answer dena ho tb to mujhe se ye question har 5 min me solve ho ja raha hai... but while verfying galat nikal raha hai....

.
.
Iss solution ka 3rd line ka "x" 4th line ka "z" ka equal(3) hai har given solution me... so plz dhyan se... bot tym waste hota hai galat question /solution k karan......
So request to all... plz give correct ans or correct the question.... :/