SOLUTION: The Rajdhani express (12437) running from Secunderabad Jn to H Nizamuddin Jn has one AC first-class coach (1A), five AC second-class (2A) coaches, and nine AC third-class (3A) coac

Question 1200119: The Rajdhani express (12437) running from Secunderabad Jn to H Nizamuddin Jn has one AC first-class coach (1A), five AC second-class (2A) coaches, and nine AC third-class (3A) coaches. Each of the 1A, 2A, and 3A coaches has a maximum capacity of 18 berths, 48 berths, and 64 berths respectively. On a given day, 10 1A berths, half of the 2A berths, and 275 3A berths were filled.
1)What is the percentage of berths filled in the train on the given day?
2)What is the relative frequency of 3A berths among total berths unfilled in the train on the given day?
Answer by textot(100) (Show Source): You can put this solution on YOUR website!
**1. Calculate Total Berths:**
* **1A:** 1 coach * 18 berths/coach = 18 berths
* **2A:** 5 coaches * 48 berths/coach = 240 berths
* **3A:** 9 coaches * 64 berths/coach = 576 berths
* **Total Berths:** 18 + 240 + 576 = 834 berths
**2. Calculate Filled Berths:**
* **1A:** 10 berths
* **2A:** (1/2) * 240 berths = 120 berths
* **3A:** 275 berths
* **Total Filled Berths:** 10 + 120 + 275 = 405 berths
**3. Calculate Percentage of Berths Filled:**
* Percentage Filled = (Total Filled Berths / Total Berths) * 100
* Percentage Filled = (405 / 834) * 100
* Percentage Filled ≈ 48.5%
**Therefore, the percentage of berths filled in the train on the given day is approximately 48.5%.**
**4. Calculate Unfilled Berths:**
* **Total Unfilled Berths:** Total Berths - Total Filled Berths = 834 - 405 = 429 berths
**5. Calculate Unfilled Berths in 3A:**
* **Unfilled 3A Berths:** Total 3A Berths - Filled 3A Berths = 576 - 275 = 301 berths
**6. Calculate Relative Frequency of Unfilled 3A Berths:**
* Relative Frequency of Unfilled 3A Berths = (Unfilled 3A Berths) / (Total Unfilled Berths)
* Relative Frequency of Unfilled 3A Berths = 301 / 429
* Relative Frequency of Unfilled 3A Berths ≈ 0.7016
**Therefore, the relative frequency of 3A berths among total unfilled berths in the train on the given day is approximately 0.7016.**

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