Raju bought 100 flower pots for rupees 8000 and Sold 20 for them at a gain of 5% . at what gain percent should be remaining pots to get a gain of 20% on the whole.
Answers
Answer:
23.75%
Step-by-step explanation:
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)
Given, Cost Price of 100 flower pots = Rs 8000
So, CP of 1 flower = Rs(8000/100) = Rs 80
CP of 80 flowers = Rs (80×80) = Rs 6400
Raju wants to gain 20% on the whole.
So, Selling Price must be (100+Profit)% of CP
= (100+20)% of 8000
= Rs 9600
He sells 20 of them at 5% gain
CP of 1 flower = Rs 80
So, CP of 20 flowers = Rs (80×20) =Rs 1600
SP at 5% profit = (105% of Rs 1600) = Rs 1680.
To sell the (100 - 20 = 80) remaining flowers to gain 20% profit overall, he must sell them for Rs (9600-1680) = Rs 7920
So, SP of 80 flowers = Rs 7920
CP of 80 flowers = Rs 6400
Gain value = Rs (7920 - 6400) = Rs 1520
Gain% = [Gain/CP× 100]%
= [1520/6400 × 100]% = 23.75%
Gain% on the 80 flowers must me 23.75%