Question

A super-Bazar prices an item in rupees and praise so that when 4 %sales tax is added, no rounding is necessary because the result is exactly in 'n' rupees, where 'n' is a positive integer. find the smallest value of 'n'.

Answer 1

10 can be the smallest value for n

Answer 2

Answer: p = 13

Assume final rupees is 'p' and initial before tax is 'x'

From the question

$x+(\frac { 4 }{ 100 } )x\quad =\quad px + (1/25) x = p$

$\frac { (25x+x) }{ 25 } \quad =\quad p$

$\frac { 26x }{ 25 } \quad =\quad p$

$x\quad =\quad \frac { 25p }{ 26 }$

Now, p must be a factor of 26 which are 1, 2, 13 and 26. For x to be terminating decimal n can be 13 or 26. 13 is smaller.

i.e. p = 13