Rekha sells a DVD player to Liza at a profit of 15% and Liza sells it Megha at a profit of 25%. If Megha pays ₹ 2875 for it, then what was the cost price for Rekha?
₹2000
Calculating Rekha's Initial Cost Price
This problem involves finding the original cost price when there are successive profit margins.
Step-by-Step Solution
- Define Variables: Let the cost price for Rekha be $C$.
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First Transaction (Rekha to Liza): Rekha sells the DVD player at a 15% profit.
- Rekha's Selling Price = Cost Price $\times$ (1 + Profit Percentage)
- Rekha's Selling Price = $C \times (1 + \frac{15}{100}) = C \times 1.15$
- This is Liza's cost price.
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Second Transaction (Liza to Megha): Liza sells it to Megha at a 25% profit.
- Liza's Selling Price = Liza's Cost Price $\times$ (1 + Profit Percentage)
- Liza's Selling Price = $(C \times 1.15) \times (1 + \frac{25}{100}) = (C \times 1.15) \times 1.25$
- This is Megha's cost price.
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Equate to Final Price: Megha pays ₹ 2875.
- $(C \times 1.15) \times 1.25 = 2875$
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Solve for $C$:
- $C \times 1.4375 = 2875$
- $C = \frac{2875}{1.4375}$
- $C = \frac{2875}{\frac{14375}{10000}}$
- $C = 2875 \times \frac{10000}{14375}$
- $C = 2875 \times \frac{16}{23}$ (Simplifying the fraction $\frac{10000}{14375}$)
- $C = 125 \times 16$
- $C = 2000$
Therefore, the cost price for Rekha was ₹ 2000.
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