By increasing the price of each ticket in the ratio 8:11, the number of tickets sold falls in the ratio 23:21. If the total revenue before the price increase was Rs. 36,800, what is the increase in revenue (in Rs.) after the change?

Introduction / Context:
In this question we apply the basic idea of percentage profit on revenue when both price and quantity sold change in a known ratio. Many aptitude exams use such ratio based questions because they test speed in handling proportional change without recomputing everything from scratch. The key is to understand that revenue is equal to price multiplied by quantity, so any combined change can be expressed as a product of two simple ratios.

Given Data / Assumptions:

Original total revenue = Rs. 36,800.
Ticket price changes in the ratio 8:11 (new price compared with old price).
Number of tickets sold changes in the ratio 23:21 (new quantity compared with old quantity).
We assume all tickets are identical and there is no other fee or tax in the calculation.
We are asked to find the increase in revenue in rupees after the change.

Concept / Approach:
Revenue R is given by R = price * quantity. When price and quantity change in known ratios, the new revenue is obtained by multiplying the original revenue by both ratios. That is, R_new = R_old * (new price / old price) * (new quantity / old quantity). Once we get the multiplication factor, we can compute the new revenue and then subtract the old revenue to obtain the increase in rupee terms.

Step-by-Step Solution:
Let original price be P and original quantity be Q, so original revenue = P * Q = 36,800. Given price ratio = 8:11, so new price = (11/8) * P. Given quantity ratio = 23:21 for old:new, so new quantity = (21/23) * Q. New revenue R_new = (11/8) * P * (21/23) * Q. Therefore R_new = P * Q * (11 * 21) / (8 * 23) = 36,800 * (231 / 184). Compute the factor: 231 / 184 = 1.25543478 approximately. Thus R_new = 36,800 * (231 / 184) = 46,200. Increase in revenue = R_new - R_old = 46,200 - 36,800 = 9,400.

Verification / Alternative check:
Instead of dealing with big numbers first, we can simplify 36,800 / 184 = 200. Then multiply 200 by 231 to get 46,200, which confirms the new revenue. Subtracting 36,800 gives 9,400 again. This cross check confirms that our ratio multiplication has been handled correctly and that no arithmetic step has been skipped.

Why Other Options Are Wrong:
Option 21250 would require a much larger multiplicative factor and does not match the product 36,800 * 231 / 184.
Option 7850 is smaller than the correct increase and does not correspond to any consistent ratio computation from the given data.
Option 12850 is also inconsistent with the exact rational factor 231 / 184 and therefore cannot be the correct increase in revenue.

Common Pitfalls:
Many students reverse the given quantity ratio and use 23/21 instead of 21/23, which flips the effect on revenue.
Some learners incorrectly add or subtract the ratios instead of multiplying them as factors on revenue.
Others mistakenly apply the ratios directly to the rupee value 36,800 without carefully separating price and quantity changes, leading to calculation errors.

Final Answer:
Therefore, the increase in revenue after the ticket price and sales change is Rs. 9,400.