A dry fruits shop sells small packets of mixed nuts for ₹150 each and large packets for ₹250 each. On one day, the owner sells 5,000 packets in total and receives ₹10.50 lakh in total sales. How many small packets does he sell that day?

Introduction:
This question tests forming a system of linear equations from a sales scenario. When two types of items are sold (small and large packets) with different prices, the total number of items and total revenue give two equations. Solving the system yields the quantity of each type. The only extra care is interpreting “₹10.50 lakh” correctly as ₹10,50,000.

Given Data / Assumptions:

• Price of small packet = ₹150
• Price of large packet = ₹250
• Total packets sold = 5,000
• Total revenue = ₹10.50 lakh = ₹10,50,000
• Let small packets = s, large packets = l

Concept / Approach:
Create two equations: s + l = 5000 and 150s + 250l = 1050000. Solve by substitution (s = 5000 - l) or elimination. Using a common factor (like dividing by 50) makes arithmetic easier and reduces mistakes.

Step-by-Step Solution:
s + l = 5000 150s + 250l = 1050000 Divide revenue equation by 50: 3s + 5l = 21000 Substitute s = 5000 - l 3(5000 - l) + 5l = 21000 15000 - 3l + 5l = 21000 2l = 6000 => l = 3000 s = 5000 - 3000 = 2000

Verification / Alternative check:
Revenue check: 2000*150 = 300000 and 3000*250 = 750000. Total = 1050000 = ₹10.50 lakh, correct. Total packets: 2000 + 3000 = 5000, correct.

Why Other Options Are Wrong:
Any other s value forces l = 5000 - s and changes the revenue away from ₹10.50 lakh. Only s = 2000 satisfies both the total packets and revenue conditions simultaneously.

Common Pitfalls:
Mistaking ₹10.50 lakh as ₹105000 (one zero missing), swapping prices of small and large packets, or forgetting that quantities must sum to 5000.

Final Answer:
He sold 2,000 small packets.