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

We are given a total of 420 tickets to sell in three batches. First, we calculate the number of tickets in each batch. Batch 1 is 'half of these tickets', so 420 / 2 = 210 tickets. These are sold at 5 rupees each, generating 210 * 5 = 1050 rupees. Batch 2 is 'one-third', so 420 / 3 = 140 tickets. These are sold at 3 rupees each, generating 140 * 3 = 420 rupees. To find the size of Batch 3 ('the rest'), we add the first two batches (210 + 140 = 350) and subtract from the total: 420 - 350 = 70 tickets. These are sold at 2 rupees each, generating 70 * 2 = 140 rupees. Finally, we add the revenue from all three batches: 1050 + 420 + 140. This sums up to 1610 rupees.