A movie was screened for 3 days – Monday, Tuesday and Wednesday. The respective ratio between the number of spectators on Monday. Tuesday and Wednesday was 2 : 3 : 5 and the price charged for three days was in the respective ratio 2 : 3 : 4. If the difference between the amount earned on Tuesday and Wednesday was Rs. 8800. What was the total amount earned in all three days? [CET—Maharashtra (MBA), 2016]

### Concept & Proportional Revenue The total amount earned is the product of the number of spectators and the ticket price. When working with ratios, we can introduce variables to find the exact algebraic amounts. $$ \text{Revenue} = \text{Number of Spectators} \times \text{Price per Ticket} $$ ### Step-by-Step Solution * **Given:** * Spectators ratio (Mon:Tue:Wed) = 2 : 3 : 5. Let the actual numbers be $2x$, $3x$, and $5x$. * Price ratio (Mon:Tue:Wed) = 2 : 3 : 4. Let the actual prices be $2y$, $3y$, and $4y$. * Calculate the revenue for each day: * Monday = $2x \times 2y = 4xy$ * Tuesday = $3x \times 3y = 9xy$ * Wednesday = $5x \times 4y = 20xy$ * We are given that the difference between Wednesday and Tuesday's earnings is Rs. 8800: * $20xy - 9xy = 8800$ * $11xy = 8800$ * $xy = 800$ * Find the total amount earned over all three days: * Total = $4xy + 9xy + 20xy = 33xy$ * Substitute the value of $xy$: * Total = $33 \times 800 = 26400$. ### Exam Strategy & Shortcut You do not need to separate $x$ and $y$. Treat $xy$ as a single unit block. The revenue ratios are directly $(2\times2) : (3\times3) : (5\times4) = 4 : 9 : 20$. The difference between Wed and Tue is $20 - 9 = 11$ units. $11 \text{ units} = 8800$, so $1 \text{ unit} = 800$. Total units = $4 + 9 + 20 = 33$. Total revenue = $33 \times 800 = 26400$. ### Common Pitfall A common mistake is assuming the multipliers for spectators and prices are the same variable ($x$), which would lead to incorrect squared terms. They are independent ratios. ### Final Answer Therefore, the correct answer is **₹ 26400**.