| A trader marked his goods at 20% above the cost price. He sold half the stock at the market price, one quarter at discount of 20% on the marked price and the rest at a discount of 40% on the market price. His total gain is |
A) 2%
B) 4.5%
C) 13.5%
D) 15%
Correct Answer: A
Solution :
| Let the total commodities \[=100\] |
| and CP (per commodity) = Rs. 100 |
| Then, total CP= Rs. 10000 |
| Now, marked price \[=100+\frac{20}{100}\times 100=\text{Rs}\text{.}\,\,\text{120}\] |
| According to the question, |
| 50% commodity sold on market price |
| \[=50\times 120=\text{Rs}\text{.}\,\,\text{6000}\] |
| 25% commodity sold on 20% discount |
| \[=25\times \left( 120-\frac{20}{100}\times 120 \right)\] |
| \[=25\times (120-24)\] |
| \[=25\times 96=\text{Rs}\text{. 2400}\] |
| 25% commodity sold on 40% discount |
| \[=25\times \left( 120-\frac{40}{100}\times 120 \right)\] |
| \[=25\times (120-48)=25\times 72=\text{Rs}\text{. 1800}\] |
| Hence, total selling price \[=1800+2400+6000\] |
| = Rs. 10200 |
| \[\operatorname{Profit}=\text{SP}-\text{CP}=10200-10000=200\] |
| \[\therefore \] Profit% =\[\frac{200}{10000}\,\times \,100\]= 2% |
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