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# MATHS SOLVED IN STEPS: Profit and Loss - 06

36.  An item was sold for Rs.27.50 with a profit of 10%. If it was sold for Rs.25.75, what would have been the percentage of profit or loss?
A. 3%                     B. 2%                   C. 4%                   D. 5%
Explanation :
SP = 27.5
Profit = 10%
CP=[100÷ (100+Profit%)]×SP
=[100÷(100+10)]×27.5
=2750÷110=25
If the item was sold for  Rs.25.75,
Gain%=[(25.75-25) ÷25]×100=[0.75÷25]×100=3%

37. Prasanth bought a car and paid 10 % less than the original price. He sold it with 30% profit on the price he had paid. What percentage of profit did he earn on the original price?
A. 17%                  B. 16%                C. 18%                D. 14%
Explanation :
Let the original price=100
Then the price at which he purchased (CP) =90% of
100=90
Profit=30%
SP=((100+Profit%)÷100)×CP
=[(100+30)÷100]×90
=[130÷100]×90=13×9=117
Required %=[(117-100) ÷100]×100=17%

38. If a seller reduces the selling price of an item from Rs.400 to Rs.380, his loss increases by 2%. What is the cost price of the item?
A. 1000                 B. 800                  C. 1200                D. 1100
Explanation :
Initial Loss% = {[ CP-400] ÷CP}×100
If the SP is reduced from 400 to 380, Loss% = [ (CP380)÷CP]×100
It is given that If the SP is reduced from 400 to 380,
Loss% increases by 2
[(CP-380)÷CP]×100- {[ CP-400] ÷CP}×100=2
(CP-380)-(CP-400)=2×[CP÷100]
20=2×[CP÷100]
CP=(20×100)÷2=1000

39. If selling price of an article is Rs. 250, profit percentage is 25%. Find the ratio of the cost price and the selling price
A. 5: 3                    B. 3 : 5                    C. 4 : 5                D. 5 : 4
Explanation :
SP = 250
Profit = 25%
CP=[100÷ (100+Profit%)]×SP
=[100÷ (100+25)]×250==[100÷125]×250=200
Required Ratio =  200 : 250 = 4:5

40. Sunil purchases two books at Rs.300 each. He sold one book 10% gain and other at 10% loss. What is the total loss or gain in percentage?
A. 10% gain            B. 1% loss              C. No loss or no gain              D. 1% gain
Explanation :
CP of two books = 300 + 300 = 600
SP of two books
= 300×(110÷100)+300×(90÷100)=(300÷100)×(110+90)=3×200=600
Total SP = Total CP
Hence No loss or no gain
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