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1. The cost price of 48 books is equal to selling price of 40 books. Find the profit %.
Sol:
48CP = 40SP

-Profit

∴ profit% = \(\frac{1}{5}\)×100 = 20%     Answer

2. The selling price of 15 article is same as the cost price of 9 article. Find the gain or loss %.
Sol:

48CP = 40SP

-Loss6

∴ Loss% = \(\frac{6}{{15}} \times 100\) = 40%    Answer

3. The ratio of CP and SP is 4:5. Find the profit %.
Sol:

-Profit1

∴ profit% = \(\frac{1}{4} \times 100\) = 25%    Answer

4. If cost price of 20 oranges is equal to the selliing price of 30 oranges. Find the profit or loss %.
Sol:
20CP = 30SP
\(\frac{{SP}}{{CP}}\) = \(\frac{2}{3}\) ⟹ Loss = 1
∴ Loss% = \(\frac{1}{3} \times 100\) = \(33\frac{1}{3}\)%       Answer

5. In selling an article for Rs. 87 there is a profit of 74%. If it is sold for Rs. 65 then find the profit or loss %.
Sol:

CP SP100 1745087××SP65

∴ profit% = \(\frac{{65 – 50}}{{50}} \times 100\) = 30%         Answer

6. If toys are bought at Rs. 10 each and sold at Rs. 9.5 each. Find the loss %.
Sol:
Loss = 9.5 – 10 = – 0.5
Loss% = \(\frac{{0.5}}{{10}} \times 100\) = 5%    Answer

7. A person sells two machines at Rs. 990 each. On one he gains 10% and on the other he loss 10%. Find the P/L% on the whole transaction.
Sol:
Method(1):
For machine ①:
gain = 10% = \(\frac{1}{{10}}\) ⟹ SP = 11 ⟶ 990
                                                               1 ⟶ 90
∴ CP₁ = 10 unit = 10 × 90 = 900
For machine ②:
Loss = 10% = \(\frac{1}{{10}}\) ⟹ SP = 9 ⟶ 990
                                                              1 ⟶ 110
∴ CP₂ = 10 unit = 10×110 = 1100
∴ total CP = 900 + 1100 = 2000
total SP = 990 + 990 = 1980
∴ Loss% = \(\frac{{2000 – 1980}}{{2000}} \times 100\)% = 1%      Answer

Method(2):

machine ①machine ②CPSP101110 9×9×9×11×1190 + 110 = 20099 + 99 = 198

∴ Loss% = \(\frac{2}{{200}} \times 100\) = 1%     Answer

Method(3):
x = 10%
Loss = \(\frac{{{x^2}}}{{100}}\)% = \(\frac{{100}}{{100}}\) = 1%     Answer

8. A house and a shop were sold for Rs. 1 lakh each. In this transaction house sale resulted into 30% loss & shop sale resulted into 30% profit. Find th P/L in the entire transaction.
Sol:
Overall Loss in entire transaction = \( – \frac{{{{30}^2}}}{{100}}\)%
= 9% Loss

now Loss = 9% = LossCPSP = 91

∴ 91 unit ⟶ 2 lakh
1 unit ⟶ \(\frac{2}{{91}}\) lakh
∴ Loss = 9 unit = 9×\(\frac{2}{{91}}\) lakh = \(\frac{{18}}{{91}}\) lakh    Answer

9. A man sells two watches for Rs. 120 each and by doing so gains 25% on one watch and loses 25% on the other. Find his loss in the whole transaction.
Sol:

Loss = = 6.25% = LossCPLossCP

∴ SP = 15 unit ⟶ 240
1 unit ⟶ 16
∴ Loss = 1 unit = 16 Rs.          Answer

10. By selling an article for Rs. 240 a man incurs a loss of 10%. At what price should he sell it, so that he makes a profit of 20%.
Sol:

\(\frac{{240}}{{90\% }} \times 120\% \) = 320 Rs.       Answer