A shopkeeper earns a profit of 40% on the cost price of an article after giving three consecutive discounts of 5%, 10% and 15% to a customer. What would have been the profit percentage, had the shopkeeper  given discounts of 5% and 10% only?

64.70%

+ 40% = \(\frac{7}{5}\)

- 5% = \(\frac{19}{20}\)

- 10% = \(\frac{9}{10}\)

- 15% = \(\frac{17}{20}\)

ATQ,

MP × \(\frac{19}{20}\) × \(\frac{9}{10}\) × \(\frac{17}{20}\) = C.P. × \(\frac{7}{5}\) = S.P.

If only 5% and 10% discount are given, then

MP × \(\frac{19}{20}\) × \(\frac{9}{10}\) = C.P. × \(\frac{7}{5}\) × \(\frac{20}{17}\) = S.P.

C.P. × \(\frac{28}{17}\) = S.P.

⇒ C.P. : S.P. = 17 : 28

Profit = 28 - 17 = 11R

Profit percent = \(\frac{11}{17}\) × 100% = 64.70%