If the cost of $15$ purses is $₹ 3750$, then the cost of $k$ purses is $₹ 500$. Find $k$.

How many of the following transactions are profitable?

$\left(i\right)$ Two tables bought for $₹ 30,500$ and sold each at $₹ 15,500$.

$\left(ii\right)$ Three fans bought for $₹ 12,500$ and sold each at $₹ 4,300$.

$\left(iii\right)$ Three shirts bought for $₹ 450$ and sold each at $₹ 1,430$.

$\left(iv\right)$ Two computers bought for $₹ 15,200$ each and sold at $₹ 38,500$.

$\left(v\right)$ A pair of denims bought for $₹ 1000$ and sold at $₹ 850$.

$\left(vi\right)$ Two mobile bought for $₹ 49,000$ and sold each at $₹ 25,300$.

Find the value of $P, Q,$ and $R$.