Rational Numbers Case Study Mathematics Class 8 | Case Study Practice PDF

Answer: (a) 420 square meters

Solution: Total area = 840 square meters. Ratio of distribution = 7:5:2. Sum of ratio parts = 7 + 5 + 2 = 14. Vegetable patch area = \(\frac{7}{14} \times 840 = \frac{1}{2} \times 840 = 420\) square meters. Therefore, 420 square meters is allocated for vegetable patches.

Answer: (a) 210 square meters

Solution: Vegetable patch area = 420 square meters. Ratio for vegetables = 3:2:1 (tomatoes:carrots:leafy greens). Sum of ratio parts = 3 + 2 + 1 = 6. Tomato area = \(\frac{3}{6} \times 420 = \frac{1}{2} \times 420 = 210\) square meters. Therefore, 210 square meters is allocated for tomatoes.

Answer: (a) 3,000 liters

Solution: Tank capacity = 3,600 liters. Water present = \(\frac{5}{6}\) of capacity. Water in tank = \(\frac{5}{6} \times 3600 = \frac{18000}{6} = 3000\) liters. Therefore, 3,000 liters of water was present in the tank.

Answer: (a) 900 liters

Solution: Tank capacity = 3,600 liters. Water used for flowers = 0.25 of tank capacity = \(0.25 \times 3600 = \frac{25}{100} \times 3600 = \frac{1}{4} \times 3600 = 900\) liters. Therefore, 900 liters was used for watering flowers.

Answer: (a) 1,050 liters

Solution: Flower bed area = \(\frac{5}{14} \times 840 = 300\) square meters. Water required per square meter = \(\frac{7}{2}\) liters per week. Total water requirement = \(300 \times \frac{7}{2} = \frac{2100}{2} = 1050\) liters. Therefore, 1,050 liters of water is required weekly for flower beds.