Question

Let ‘R’ be the ratio of Foreign Exchange Earnings from Tourism in India (in US million) to Foreign Tourist Arrivals in India (in million). Assume that R increases linearly over the years. If we draw a pie chart of R for all the years, the angle subtended by the biggest sector in the pie chart would be approximately:

• A. 24
• B. 30
• C. 36
• D. 42
• E. 48

Hint:

In AP-based pie chart problems, the maximum slice angle is found by $\tfrac{R_{\max}}{\text{Sum of AP}} \times 360^\circ$. You do not need exact values if the sequence is evenly increasing — approximation suffices.

Answer 1

The Correct Option is C

Step 1: Define $R$.
\[ R = \frac{\text{Foreign Exchange Earnings (US \$ million)}}{\text{Foreign Tourist Arrivals (million)}}. \] This represents the average earnings per foreign tourist in US dollars.
Step 2: Given assumption.
The problem states that $R$ increases linearly with the years (1997–2011, i.e., 15 years).
Thus, we can treat the $R$ values as an arithmetic progression AP).
Step 3: Biggest sector in pie chart.
When we draw a pie chart, the angle corresponding to each year is proportional to $R$ for that year.
Since $R$ is in AP, the maximum $R$ corresponds to the last year (2011).
The angle subtended by the largest sector is: \[ \theta = \frac{R_{\max}}{\sum_{i=1}^{15} R_i}\times 360^\circ. \] Step 4: Simplify using AP sum.
For an AP:
- $R_{\max}=a+(n-1)d$,
- Sum $S_n=\frac{n}{2}A+R_{\max})$.
So, \[ \theta = \frac{R_{\max}}{S_n}\times 360 = \frac{R_{\max}}{\tfrac{n}{2}A+R_{\max})}\times 360. \] Since $R_{\max}$ and $a$ are of similar magnitude and $n=15$, the approximate result is: \[ \theta \approx 36^\circ. \] \[ \boxed{36^\circ} \]