A shopkeeper promises to sell his good at x% profit but he uses 20% less weight while selling. Total gain is 56\(\frac{1}{4}\)%. Find the value of x?

25%

let x% profit = \(\frac{b}{a}\)

                     C.P      :     S.P

Profit :             a      :       b

Weight:          800   :     1000  

Total Profit :    16    :        25                (+ 56\(\frac{1}{4}\)% = \(\frac{9}{16}\))

\(\frac{800a}{1000b}\) = \(\frac{16}{25}\)

\(\frac{a}{b}\) = \(\frac{4}{5}\)

a : b = 4 : 5

x% = \(\frac{1}{4}\) × 100% = 25%