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# MATHS SOLVED IN STEPS: Profit and Loss - 03

21. An exporter expects a gain of 22.5% on his cost price. If in a week, his sale was of Rs. 392, what was his profit?
A. Insufficient Data          B. Rs. 80        C. Rs. 90          D. Rs. 72
Explanation :
SP=392
Gain=22.5%
CP=(100÷(100+Gain%))×SP
=(100÷(100+22.5))×392
=(100÷122.5)×392
=(1000÷1225)×392
=(40÷49)×392
=(40÷7)×56
=40×8
=320
Profit=SP-CP=392-320=72

22. The percentage profit earned by selling an item for Rs. 1920 is equal to the percentage loss incurred by selling the same item for Rs. 1280. At what price should the item be sold to make 25% profit?
A. Insufficient Data         B. Rs. 3000           C. Rs. 2000              D. Rs. 2200
Explanation :
Let CP = x
Percentage profit earned by selling an item for Rs. 1920
= ( (SP-CP)÷CP)×100
= ((1920-x)÷x)×100
Percentage loss incurred by selling the same item for Rs. 1280
=((SP-CP)÷CP)×100= ((x-1280)÷x)×100
Given that Percentage profit earned by selling an item for Rs. 1920=Percentage loss incurred by selling the same item for Rs. 1280
((1920-x)÷x)×100=((x-1280)÷x)×100
(1920-x)÷x=(x-1280)÷x
1920–x = x–1280
2x=1920+1280=3200
x=3200÷2=1600
Required Selling Price=CP×(125÷100)
=1600×(125÷100)=1600×(5÷4)=400×5=2000

23. A man buys a scooter for Rs. 1400 and sells it at a loss of 15%. What is the selling price of the scooter?
A. Rs. 1240        B. Rs. 1190           C. Rs. 1090               D. Rs. 1130
Explanation :
SP=1400×(85÷100)=14×85=1190

24. Murali purchased 20 dozens of toys at the rate of Rs. 375 per dozen. He sold each one of them at the rate of Rs. 33. Find out his profit percentage
A. 3.5                 B. 5.6               C. 4.1           D. 3.4
Explanation :
CP of 1 toy=(375÷12)
SP of 1 toy=33
Profit=SP-CP
=33-(375÷12)
Profit%=(Profit÷CP)×100
={(33-(375÷12)) ÷(375÷12)}×100
=(33×(12÷375)-1)×100
=(33×(4÷125)-1)×100
=(7÷125)×100
=(7÷5)×4
=28÷5
=5.6%

25. Some items were bought at 6 items for Rs. 5 and sold at 5 items for Rs. 6. What is the gain percentage?
A. 44%                 B. 3313               C. 3123             D. 30%
Explanation :
CP of 1 item=5÷6
SP of 1 item=6÷5
Gain%=((SP-CP)÷CP)×100
={((6÷5)-(5÷6)) ÷(5÷6)}×100
={(36÷25-1)}×100
=(11÷25)×100
=11×4=44
* MATHS (SOLVED IN STEPS ==> Ratio and Proportion
* MATHS (SOLVED IN STEPS ==> Progressions
* MATHS (SOLVED IN STEPS ==> Percentage
* MATHS (SOLVED IN STEPS ==> Surds and Indices
* MATHS (SOLVED IN STEPS ==> Calendar
* MATHS (SOLVED IN STEPS ==> Square and cube
* MATHS (SOLVED IN STEPS ==> Simplification
* MATHS (SOLVED IN STEPS ==> Problems on Average
* MATHS (SOLVED IN STEPS ==> HCF & LCM
* MATHS (SOLVED IN STEPS ==> Problems on Trains
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* MATHS (SOLVED IN STEPS ==>