To find the total cost, we need to calculate the cost of apples and oranges separately and then add them together.
Step 1: Calculate the cost of apples.
Given: 5 kg of apples at Rs. 20 per kg.
Cost of apples = 5 kg × Rs. 20/kg = Rs. 100.
Step 2: Calculate the cost of oranges.
Given: 3 kg of oranges at Rs. 30 per kg.
Cost of oranges = 3 kg × Rs. 30/kg = Rs. 90.
Step 3: Calculate the total cost.
Total cost = Cost of apples + Cost of oranges = Rs. 100 + Rs. 90 = Rs. 190.
Therefore, the total cost is Rs. 190.
For any natural number $k$, let $a_k = 3^k$. The smallest natural number $m$ for which \[ (a_1)^1 \times (a_2)^2 \times \dots \times (a_{20})^{20} \;<\; a_{21} \times a_{22} \times \dots \times a_{20+m} \] is: