Question

If a,b,c,d are integers, then what 4 digit number abcd satisfies the equation 4 x abcd =dcba

Answer 1

abcd x 4=dcba

=> a is an even number

It can be 0,2,4,6,8

It can’t be 0 as then abcd won’t be a 4 digit number

It cant be 4,6,8 or else abcd x 4 will become a 5 digit number

=> a=2

for 4d to have 2 in units place d can be either 3 or 8

It cant be 3 as then 4a>d (at the thiusanth place)

=> d=8

b = units place of 3 + 4c (3 is carried over from multiplication of 4 with d)

=> b is odd number

It can be 1,3,5,7,9

d = 4a + carryover from hundredth place(4b + carryover from tenth place)

but as d=8 and a = 2 the carryover from hundredth place(4b + carryover from tenth place) term should be zero

=> b=1 ; as for all other cases there will be a carryover

1 is units place of 3+ 4c

=>8 is unit place of 4c

=> c can be 2 or 7

Hence answer is among 2128 and 2178

By substitution we see only 2178 satisfies the criteria

Hope it helps