1. Last year, 3 buses carried a total of 162 students and teachers for a school trip, and all buses were full. This year there are 204 students. Assuming the same bus capacity as last year, how many buses are needed this year, and will every bus be full?

2. The area of Delhi is 1,484 sq. km and the area of Mumbai is 550 sq. km. The population of Delhi is approximately 30 million and that of Mumbai is 20 million. Which city is more crowded and why?

3. A crane is 155 cm tall, and the ratio of the length of its neck to the rest of its body is 4:6. If a person’s neck and the rest of the body also have this ratio, what fraction of the person’s total height would be the length of the neck?

4. In Lilavati, “If 2 1/2 palas of saffron cost 3 niskas, what quantity of saffron can be bought for 9 niskas?”

5. Harmain is a 1-year-old girl. Her elder brother is 5 years old. After how many years will the ratio of Harmain’s age to her brother’s age become 1:2, and how old will Harmain be then?

6. The mass of equal volumes of gold and water are in the ratio 37:2. If the mass of 1 litre of water is 1 kg, what is the mass of 1 litre of gold?

7. It is good farming practice to apply 10 tonnes of cow manure per acre of land. A farmer plans to grow tomatoes in a plot of size 200 ft by 500 ft. Approximately how much manure should he buy for this plot?

8. A tap takes 15 seconds to fill a mug of water whose volume is 500 mL. How much time will the same tap take to fill a bucket of water if the bucket has a 10-litre capacity?

9. One acre of land costs ₹15,00,000. What is the cost of 2,400 square feet of the same land?

10. A pair of oxen takes 6 hours to plough an acre of land. A tractor can plough the same area 4 times faster than a pair of oxen. For a 20-acre field, how long will it take using the pair of oxen, and how long using the tractor?