A shopkeeper promises to sell his goods at x% profit but he uses 20% less weight and also gain  \(37\frac{1 }{2}\) %. Find x.

10%

Let actual weight = 1000 gm

& CP of 100 gm is 1000 Rs.

CP of 1 gm is 1 Rs.

                         = 1000 × \(\frac{80}{100}\) = 800 gm

                   CP = 800 Rs.

              37\(\frac{1}{2}\) = \(\frac{3}{8}\)

CP = 8P, SP = 11P

8P = 800 ⇒ P = 100

SP = 11P = 1100

CP = 1000

Loss = 1100 - 1000 = 100

Loss % = \(\frac{100}{1000}\) × 100 = 10% = x%