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# MATHS SOLVED IN STEPS: Profit and Loss - 04

26. 100 oranges were bought at the rate of Rs. 350 and sold at the rate of Rs. 48 per dozen. What is the percentage of profit or loss?
A. 11.29% Loss                  B. 11.14% Profit
C. 14.29% Profit                D. 14.29% Loss
Explanation :
CP of 100 oranges=350
CP of 1 orange=350÷100=3.5
SP of 12 oranges=48
SP of 1 orange=48÷12=4
Profit%={(SP-CP)÷CP}×100
={(4-3.5)÷3.5}×100= (.5÷3.5)×100=(1÷7)×100=100÷7=14.29

27. On selling 17 balls at Rs. 720, there is a loss equal to the cost price of 5 balls. What is the cost price of a ball?
A. Rs. 43                 B. Rs. 60                C. Rs. 55         D. Rs. 34
Explanation :
Loss = (CP of 17 balls) - (SP of 17 balls) = (CP of 17 balls) - 720
Given that Loss = (CP of 5 balls)
=> (CP of 17 balls) - 720 = (CP of 5 balls) => (CP of 17 balls) - (CP of 5 balls) = 720
=> CP of 12 balls = 720
=> CP of 1 ball=720÷12=60

28. When an item is sold for Rs. 18,700, the owner loses 15%. At what price should that plot be sold to get a gain of 15%?
A. Rs. 25100       B. Rs. 24200    C. Rs. 25300     D. Rs. 21200
Explanation :
When an item is sold for Rs. 18,700, the owner loses 15%SP = 18700 and Loss=15%
CP={100÷(100 -Loss%)}×SP
={100÷ (100"15)}×18700={100÷85}×18700
To get a gain of 15%, SP ={(100+Gain%)÷100}×CP
={(100+15)÷100}×CP
=(115÷100)×CP
={(115÷100)×(100÷85)}×18700=(115÷85)×18700=(23÷17)×18700
=23×1100=25300

29. A trader mixes 26 kg of rice at Rs. 20 per kg with 30 kg of rice of other variety at Rs. 36 per kg and sells the mixture at Rs. 30 per kg. What is his profit percentage?
A. 6%          B. 5%                 C. 4%              D. 7%
Explanation :
CP of 1st variety rice=20
CP of 2nd variety rice=36
CP of the 56 kg rice mixture=(26×20+30×36)=520+1080=1600
SP of the 1 kg rice mixture=30
SP of the 56 kg rice mixture=30×56=1680
Gain=SP-CP=1680-1600=80
Gain%=(Gain÷CP)×100=(80÷1600)×100=5%

30. If a material is sold for Rs.34.80, there is a loss of 25%. Find out the cost price of the material?
A. Rs.46.40               B. Rs.44                C. Rs.42              D. Rs.47.20
Explanation :
SP=34.80
Loss=25%
CP={100÷ (100-Loss%)}×SP
=[100÷ (100-25)]×34.80=(100÷75)×34.80
=[4×34.80]÷3
=4×11.60=46.40
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