Question

A super-bazar prices an item in rupees and paise 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

let the final rupees of an item be n

let the initial rupees before tax be x

sales tax = 4%

initial rupees + sales tax= final rupees

x+ 4/100x=n

x+1/25x=n

26/25x=n

x=n25/26

here , n should be the factor of 26.

so the factor of 26 are, 1,2,13,26.

for x to be terminating decimal , n can either be 13,or 26 . 13 is smaller

therefore , n= 13.

hope it helps

Answer 2

let cp=x

sales tax =4%

x+4x÷100=n

104x÷100=n

x=25n÷26

n=13