Find the smallest number such that if its rightmost digit is placed at its left end, the new number so formed is precisely 50% larger than the original number.

ans: 285714

can get it by solving :

10*m+c= 2/3*( c*10^k+m)

which transforms into:

28m=2c*10^k-3c

which leads to :

28*m=c*199....97

hence c=4 m=28571

and the combined number 428571

OR c=8 m=57142

and the combined number 571428

Another method is by looking at the multiples of the periodic decimal representation of 1/7:

1 142857

2 285714

3 428571

4 571428

5 714285

6 857142

HERE YOU CLEARLY SEE BOTH ANSWERS

i.e. 2/7=>3/7 and 4/7=>6/7

since the problem requested the smallest number

the answer is 285714 .

ady