P sells an item to Q at 47% profit. Q sells the same item to R at 50% loss. If R paid Rs. 6027 for the item, then at what price (in Rs.) is the item purchased by P?

Correct option is D

Given:
P sells to Q at 47% profit.
Q sells to R at 50% loss.
R paid ₹6027 for the item.
Formula Used:
Selling Price = Cost Price × (1 + Profit Percentage / 100)
Selling Price = Cost Price × (1 - Loss Percentage / 100)
Solution:
Let the cost price at which P purchased the item be P
It is given that Q sold the item to R at a loss of 50% and the selling price to R was ₹6027.
  $$\begin{align*}\text{Q's cost price} \times \left(1 - \frac{50}{100} \right) &= 6027 \\\text{Q's cost price} \times 0.50 &= 6027 \\\text{Q's cost price} &= \frac{6027}{0.50} = ₹12054\end{align*}$$​​
Now, since P sold the item to Q at a profit of 47%, the cost price of Q is the same as the selling price of P.
​$$\begin{align*}P \times \left(1 + \frac{47}{100} \right) &= 12054 \\P \times 1.47 &= 12054 \\P &= \frac{12054}{1.47} = ₹8200\end{align*}$$ ​

Alternate Solution:  ​
Let the Cost Price be P 
 $$\begin{align*}P \times \frac{147}{100} \times \frac{50}{100} &= 6027 \\P \times \frac{7350}{10000} &= 6027 \\ P = ₹8200\end{align*}$$​​