| Direction: In each of the following questions read the given statements and compare the given two quantities on its basis. |
| The cost prices of two items x and y are the same. The shopkeeper decided to mark the price 50% more than the cost price of each item. A discount of 15% was given on item x and a discount of 10% was given on item y. Total profit earned on both the items was Rs. 50. |
| Quantity I. Cost price of either item. |
| Quantity II. Cost price of any other item which was sold at 10% profit and the profit earned on it was Rs. 9. |
A) Quantity I > Quantity II
B) Quantity I \[\ge \] Quantity II
C) Quantity I \[\le \] Quantity II
D) Quantity I < Quantity II
E) No relation between Quantity I and II
Correct Answer: D
Solution :
Item x Item y CP CP MP \[CP\times \frac{150}{100}\] \[CP\times \frac{150}{100}\] SP \[CP\times \frac{3}{2}\times \frac{85}{100}\] \[CP\times \frac{3}{2}\times \frac{90}{100}\] According to the question, \[\left( \frac{51}{40}CP-CP \right)+\left( \frac{27}{20}CP-CP \right)=50\] or, \[\frac{11CP}{40}+\frac{7}{20}CP=50\] or, \[\frac{11CP+14CP}{40}=50\] or, \[\frac{25CP}{40}=50\] or, \[CP=Rs.\,80\] Quantity I. Cost price of either item = Rs. 80 Quantity II. 10% of CP = 9 \[\therefore \]\[CP=\frac{9\times 100}{10}=Rs.\,90\] Hence Quantity I < Quantity II
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