8️⃣ A train crosses a pole in 10 seconds and a platform of length 100 meters in 20 seconds. What is the length of the train?
Step-by-Step Explanation
Let the length of the train be 'L' meters.
Speed of the train = L / 10 m/s.
When crossing the platform, (L + 100) / 20 = L / 10.
10(L + 100) = 20L.
10L + 1000 = 20L.
10L = 1000.
L = 100 meters.
Answer: 100 meters ✅
9️⃣ Two trains start from stations A and B and travel towards each other at speeds of 50 km/h and 60 km/h respectively. At the time of their meeting, the second train has traveled 120 km more than the first. What is the distance between A and B?
Step-by-Step Explanation
Let the time taken for them to meet be 't' hours.
Distance traveled by the first train = 50t km.
Distance traveled by the second train = 60t km.
60t - 50t = 120 km.
10t = 120.
t = 12 hours.
Distance between A and B = (50 * 12) + (60 * 12).
Distance = 600 + 720.
Distance = 1320 km.
Answer: 1320 km ✅
🔟 A, B, and C undertook to complete a work for ₹5,750. A and B together can complete 19/23 of the total work, and B and C together can complete 8/23 of the total work. What is the share of B in the total wages?
Step-by-Step Explanation
1. Work done by A: 1 - 8/23 = 15/23
2. Work done by C: 1 - 19/23 = 4/23
3. Work done by B: 1 - (15/23 + 4/23) = 1 - 19/23 = 4/23
4. Ratio of work done by A:B:C: 15/23 : 4/23 : 4/23, which simplifies to 15:4:4