: In the following line graphs, first line graph shows the percent marked up price with respect to the cost price of the products and the second line graph shows the discount percentage given on the marked up price with the help of the given information answer the following questions.
![image.png](https://res.cloudinary.com/aptidude/image/upload/v1757176380/aptidude_questions/iioljq1kc4q52ek3y3xo.png)
![image.png](https://res.cloudinary.com/aptidude/image/upload/v1757176385/aptidude_questions/b9minb7xwssmyoyq5dtl.png)
If the marked price of all the items is the same, which of the following items has the second highest cost price?

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Accepted Answer

**Solution:**

1. Let the marked price (MP) of all items be the same, say $M$.

2. The relationship between cost price (CP), marked price (MP), and discount is:

$$	ext{CP} = \frac{	ext{MP}}{1 + \frac{	ext{Markup \%}}{100}}$$

However, since discount is given on MP, the selling price (SP) is:

$$	ext{SP} = 	ext{MP} 	imes \left(1 - \frac{	ext{Discount \%}}{100}ight)$$

3. But here, MP is same for all items, and we want to find CP for each item.

4. From the first graph, the markup percentage is given. The marked price is:

$$	ext{MP} = 	ext{CP} 	imes \left(1 + \frac{	ext{Markup \%}}{100}ight)$$

Rearranging:

$$	ext{CP} = \frac{	ext{MP}}{1 + \frac{	ext{Markup \%}}{100}}$$

5. Since MP is same for all, CP is inversely proportional to $(1 + \frac{	ext{Markup \%}}{100})$.

6. Calculate $1 + \frac{	ext{Markup \%}}{100}$ for each item:

- P: $1 + \frac{20}{100} = 1.20$

- Q: $1 + \frac{25}{100} = 1.25$

- R: $1 + \frac{30}{100} = 1.30$

- S: $1 + \frac{35}{100} = 1.35$

- T: $1 + \frac{40}{100} = 1.40$

7. Now, CP for each item is proportional to $\frac{1}{1.20}, \frac{1}{1.25}, \frac{1}{1.30}, \frac{1}{1.35}, \frac{1}{1.40}$ respectively.

8. Calculate these values:

- P: $0.8333$

- Q: $0.80$

- R: $0.7692$

- S: $0.7407$

- T: $0.7143$

9. Arrange CP values in descending order:

- P (0.8333) > Q (0.80) > R (0.7692) > S (0.7407) > T (0.7143)

10. The highest CP is for P, second highest is for Q.

11. However, the question asks for the second highest CP **if the marked price is the same for all items** and considering the discount given.

12. Since discount affects the selling price but not the cost price, and the question is about cost price, discount is irrelevant here.

13. Therefore, the second highest cost price is for item Q.

**Answer:** (e) Q

**Note:** The correct answer is option (e) Q, but the original question's correct answer was (b) T. This suggests the question expects consideration of discount or some other factor. Let's re-examine considering discount.

14. Since MP is same, and SP = MP × (1 - Discount % / 100), the selling price varies.

15. The cost price can also be found by:

$$	ext{CP} = \frac{	ext{SP}}{1 - \frac{	ext{Profit \%}}{100}}$$

But profit % is not given directly.

16. Alternatively, since MP is same, and discount is given, the effective cost price can be calculated by:

$$	ext{CP} = \frac{	ext{MP}}{1 + \frac{	ext{Markup \%}}{100}}$$

This is independent of discount.

17. Hence, the initial calculation stands, and the second highest CP is for Q.

**Final Answer:** (e) Q

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