Question

Kamini bought 100 pots for 3 8000 and sold 20 of these at a gain of 5%. At what gain
per cent should she sell the remaining pot to get a gain of 20% on the whole?
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Answer 1

Answer:

CP of 100 flower pots in Rupees = 8000

=> CP of 1 pot = 80

20 pots were sold at a gain of 5%

CP of 20 pots = 80*20 = 1600

=> SP of 20 pots = CP of 20 pots + 5% of CP of 20 pots

=> SP of 20 pots = 1600 + 5% of 1600

=> SP of 20 pots = 1.05*1600 = 1680

Overall gain = 20%

=> SP of 100 pots = CP of 100 pots + 20% of CP of 100 pots

CP of 100 pots = 8000

=> SP of 100 pots = 8000 + 20% of 8000

=> SP of 100 pots = 1.2*8000 = 9600

Now,

20 pots have been sold for 1680

=> Remaining 80 pots will have to be sold for 9600 - 1680 = 7920

=> SP of 80 pots = 7920

=> SP of 1 pot = 99

We know that CP of 1 pot = 80

=> % gain = 100*(99 - 80)/80 = 23.75

The remaining pots will have to be sold at a profit of 23.75%

Verification:

CP of 100 pots = 8000

SP of 20 pots = 1680

SP of remaining 80 pots = 7920

SP of 100 pots = 1680 + 7920 = 9600

Overall Profit% = 100*(9600 - 8000)/8000 = 100*(1600/8000)

= 100*(1/5) = 20 (as given in the problem, hence verified)