1. If a model car is 50 times smaller than a real car,
(a) 100 cm on the real car would be represented by how much on the model?
(b) What length on the real car does 6 cm on the model represent?
2. Ram and his sister Kalpana win a prize of Rs 2000. They decide to share the prize in the ratio of their ages. Ram is 15 years old and Kalpana is 10 years old. How much do each of them receive?
(b) Binod and his elder brother Kapil win a prize of Rs 6000. They decide to share the prize in the ratio of their ages. Binod is 28 years old and Kapil is 32 years old. How much do each of them receive?
Answer (2)
The model car length corresponding to 100 cm on the real car is calculated by dividing 100 by the scaling factor 50: 50 100 = 2 cm.
The real car length corresponding to 6 cm on the model car is calculated by multiplying 6 by the scaling factor 50: 6 × 50 = 300 cm.
Ram's share of the prize money is calculated as 2000 × 25 15 = 1200 Rs, and Kalpana's share is 2000 × 25 10 = 800 Rs.
Binod's share of the prize money is calculated as 6000 × 60 28 = 2800 Rs, and Kapil's share is 6000 × 60 32 = 3200 Rs. The final answers are: 2 cm, 300 cm, 1200 Rs, 800 Rs, 2800 Rs, 3200 Rs.
Explanation
Problem Analysis We are given a problem involving scaling, ratios, and prize sharing. We need to determine the corresponding length on a model car for a given length on a real car, the length on a real car for a given length on a model car, and how to divide prize money between people based on their ages.
Model Car Length Calculation (a) The model car is 50 times smaller than the real car. Therefore, 100 cm on the real car would be represented by 50 100 cm on the model car. 50 100 = 2 So, 100 cm on the real car is represented by 2 cm on the model car.
Real Car Length Calculation (b) Since the model car is 50 times smaller than the real car, 6 cm on the model car represents 6 × 50 cm on the real car. 6 × 50 = 300 Therefore, 6 cm on the model car represents 300 cm on the real car.
Ram and Kalpana Prize Sharing Ram and Kalpana win a prize of Rs 2000, and they decide to share the prize in the ratio of their ages. Ram is 15 years old, and Kalpana is 10 years old. The total age ratio is 15 + 10 = 25 . Ram's share is 25 15 of the total prize, and Kalpana's share is 25 10 of the total prize. Ram's share: 2000 × 25 15 = 2000 × 5 3 = 1200 Kalpana's share: 2000 × 25 10 = 2000 × 5 2 = 800 Ram receives Rs 1200, and Kalpana receives Rs 800.
Binod and Kapil Prize Sharing Binod and Kapil win a prize of Rs 6000, and they decide to share the prize in the ratio of their ages. Binod is 28 years old, and Kapil is 32 years old. The total age ratio is 28 + 32 = 60 . Binod's share is 60 28 of the total prize, and Kapil's share is 60 32 of the total prize. Binod's share: 6000 × 60 28 = 100 × 28 = 2800 Kapil's share: 6000 × 60 32 = 100 × 32 = 3200 Binod receives Rs 2800, and Kapil receives Rs 3200.
Final Answer (a) 100 cm on the real car is represented by 2 cm on the model car. (b) 6 cm on the model car represents 300 cm on the real car. Ram receives Rs 1200, and Kalpana receives Rs 800. Binod receives Rs 2800, and Kapil receives Rs 3200.
Examples
Understanding ratios and proportions is crucial in many real-life scenarios. For instance, when scaling recipes, you need to maintain the correct ratios of ingredients to ensure the dish tastes as expected. Similarly, in business, profit sharing among partners often depends on pre-agreed ratios based on investment or work input. These mathematical concepts help ensure fairness and accuracy in various distributions and scaling problems.
The model car represents 100 cm on the real car as 2 cm, and 6 cm on the model corresponds to 300 cm on the real car. Ram receives Rs 1200 and Kalpana receives Rs 800 from their prize, while Binod gets Rs 2800 and Kapil receives Rs 3200 from theirs. All distributions are based on their respective ages.
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