Ravi has two examinations on Wednesday - Engineering Mathematics in the morning and Engineering Drawing in the afternoon. He has a fixed amount of time to read the textbooks of both these subjects on Tuesday. During this time he can read $80$ pages of Engineering Mathematics and $100$ pages of Engineering Drawing. Alternatively, he can also read $50$ pages of Engineering Mathematics and $250$ pages of Engineering Drawing. Assume that the amount of time it takes to read one page of the textbook of either subject is constant. Ravi is confident about Engineering Drawing and wants to devote full time to reading Engineering Mathematics. The number of Engineering Mathematics text book pages he can read on Tuesday is

Concept & Formula This problem is solved using **Linear Equations & Ratios**. Since the total time available is constant in both scenarios, we can equate the two scenarios to find the reading speed ratio between the two subjects. Once we know the "exchange rate" between pages of Drawing and pages of Mathematics, we can convert all his time into Mathematics. Step-by-Step Solution * **Defining Variables:** Let $t_m$ be the time taken to read $1$ page of Math. Let $t_d$ be the time taken to read $1$ page of Drawing. Let $T$ be the total fixed time available on Tuesday. * **Setting up Equations:** Scenario 1: $T = 80t_m + 100t_d$ Scenario 2: $T = 50t_m + 250t_d$ * **Finding the Time Ratio:** Since the total time is the same, equate the two expressions: $80t_m + 100t_d = 50t_m + 250t_d$ $30t_m = 150t_d$ $t_m = 5t_d$ This means reading $1$ page of Math takes the same amount of time as reading $5$ pages of Drawing. * **Calculating Full Capacity for Math:** Ravi wants to spend ALL his time on Math. Take Scenario 1: He currently reads $80$ pages of Math + $100$ pages of Drawing. Convert the Drawing pages into equivalent Math pages based on time. Since $5$ Drawing pages = $1$ Math page, $100$ Drawing pages = $\frac{100}{5} = 20$ Math pages. Total Math pages = $80 + 20 = 100$. Exam Strategy & Shortcut Use the **Delta Method**. Observe the changes between the two scenarios directly: To increase Drawing pages from $100$ to $250$ (an increase of $+150$ Drawing pages), Ravi had to drop his Math pages from $80$ to $50$ (a decrease of $-30$ Math pages). So, $30$ Math pages = $150$ Drawing pages. Ratio: $1$ Math page = $5$ Drawing pages. To get maximum Math pages, convert the remaining $100$ Drawing pages from the first scenario into Math: $100 / 5 = 20$. Add this to the existing $80$ Math pages to get $100$. Common Pitfall Assuming reading speeds are identical for both subjects. The text explicitly says the time to read one page is constant *within* a subject, not *across* subjects. You must find the ratio. Final Answer Therefore, the correct answer is **100**.