Understanding the Problem

This problem involves a chain of transactions where a laptop's price changes due to profit and loss percentages. We are given the final price paid by the last person (R) and need to work backward to find the initial cost price for the first seller (P).

Key Information Provided

• P sold the laptop to Q at a loss of 25%.
• Q sold the laptop to R at a profit of 20%.
• R purchased the laptop for ₹22,500.
• We need to find the original cost price for P.

Step-by-Step Calculation

Calculating Q's Selling Price (which is R's Cost Price)

We know that Q sold the laptop to R at a profit of 20%. This means R's cost price is 120% of Q's cost price.

Let $C_Q$ be the cost price for Q.

R's Cost Price ($C_R$) = $C_Q \times (1 + \text{Profit Percentage})$

$C_R = C_Q \times (1 + 20/100)$

$C_R = C_Q \times (1 + 0.20)$

$C_R = C_Q \times 1.20$

We are given that $C_R = 22,500$. So,

$22,500 = C_Q \times 1.20$

Now, we can find $C_Q$:

$C_Q = 22,500 / 1.20$

$C_Q = 22500 / (12/10)$

$C_Q = 22500 \times (10/12)$

$C_Q = 22500 \times (5/6)$

$C_Q = (22500 / 6) \times 5$

$C_Q = 3750 \times 5$

$C_Q = 18,750$

So, Q's cost price was ₹18,750.

Calculating P's Cost Price

P sold the laptop to Q at a loss of 25%. This means Q's cost price ($C_Q$) is 75% of P's original cost price ($C_P$).

$C_Q = C_P \times (1 - \text{Loss Percentage})$

$C_Q = C_P \times (1 - 25/100)$

$C_Q = C_P \times (1 - 0.25)$

$C_Q = C_P \times 0.75$

We found that $C_Q = 18,750$. Substituting this value:

$18,750 = C_P \times 0.75$

Now, we can find $C_P$:

$C_P = 18,750 / 0.75$

$C_P = 18750 / (75/100)$

$C_P = 18750 \times (100/75)$

$C_P = 18750 \times (4/3)$

$C_P = (18750 / 3) \times 4$

$C_P = 6250 \times 4$

$C_P = 25,000$

Conclusion

The original cost price of the laptop for P was ₹25,000.