A shopkeeper advertises for selling cloth at 7% loss. However, by using a false scale of length 1 metre he actually gains 24%. What will be the actual length he uses instead of 1 metre ?

75 cm

Let C.P of 1 m cloth = Rs. 1

Professed S.P of 1 m cloth = Rs. \(\frac{93}{100}\) = Rs. 0.93

Profit earned = 24%

⇒ Actual C.P of cloth sold for Rs. 0.96 =\(\frac{100}{124}\) ×0.93 = Rs.0.75

∴ Actual length of scale = Length bought for Rs. 0.75 = 75 cm.