For a charity show, the total tickets sold were 420. Half of these tickets were sold at the rate of Rs 5 each, one-third at the rate of Rs 3 each and the rest for Rs 2 each. What was the total amount received?

Correct Option (C)

The total number of tickets sold for the charity show was 420.

• Half of the tickets were sold at Rs 5 each: $\frac{420}{2}$ = 210 tickets. The revenue generated from these tickets was 210 × ₹5 = ₹1050.
• One-third of the tickets were sold at Rs 3 each: $\frac{420}{3}$ = 140 tickets. The revenue generated from these tickets was 140 × ₹3 = ₹420.
• The remaining tickets were sold at Rs 2 each: The number of remaining tickets was 420 – 210 – 140 = 70 tickets. The revenue generated from these tickets was 70 × ₹2 = ₹140.

The total amount received from the sale of all tickets is the sum of the revenues from each category:

Total amount = ₹1050 + ₹420 + ₹140 = ₹1610.

Incorrect Options:

Options A (Rs 900), B (Rs 1,540), and D (Rs 2,000) are incorrect. The accurate calculation of the total amount received involves segmenting the total number of tickets according to their respective selling prices and summing the individual revenues. The detailed computation demonstrates that the correct total revenue is ₹1610, which does not align with these alternative values.