If you happen to be viewing the article Vimla started a business investing Rs 90000. After 3 months, Pulkit joined him with a capital of Rs. 120000. After another 6 months, Alia joined them with a capital of Rs. 180000. At the end of the year, they made a profit of Rs. 40000. What would be Alia’s share in it? ? on the website Math Hello Kitty, there are a couple of convenient ways for you to navigate through the content. You have the option to simply scroll down and leisurely read each section at your own pace. Alternatively, if you’re in a rush or looking for specific information, you can swiftly click on the table of contents provided. This will instantly direct you to the exact section that contains the information you need most urgently.
Vimla invested Rs. 90,000 in a business, and later Pulkit (Rs. 120,000) and Alia (Rs. 180,000) joined. They ended up making a profit of Rs. 40,000 by the year-end. Discover how much of that profit goes to Alia!
Vimla started a business investing Rs 90000. After 3 months, Pulkit joined him with a capital of Rs. 120000. After another 6 months, Alia joined them with a capital of Rs. 180000. At the end of the year, they made a profit of Rs. 40000. What would be Alia’s share in it?
Alia’s share in the profit is Rs.8000
Explanation
Alia’s share in the profit will be based on the ratio of her investment to the total investment and the duration of her investment.
Here’s how to calculate Alia’s share:
Calculate the investment ratio:
Investment ratio: Vimla : Pulkit : Alia = (90000 * 12) : (120000 * 9) : (180000 * 6) = 2 : 2 : 1
- Vimla: Invested Rs. 90,000 for 12 months (1 year).
- Pulkit: Invested Rs. 120,000 for 9 months (1 year – 3 months).
- Alia: Invested Rs. 180,000 for 6 months (1 year – 3 months – 6 months).
Calculate Alia’s share:
- Alia’s share = Total profit * (Alia’s investment ratio)
- Alia’s share = Rs. 40,000 * (1/5)
- Alia’s share = Rs. 8,000
Therefore, Alia’s share in the profit would be Rs. 8,000
Ratio and Proportion in Mathematics
Ratios and proportions are fundamental concepts in mathematics that deal with comparing quantities. They are used in various branches of mathematics, including algebra, geometry, and trigonometry, and have numerous applications in real-world scenarios.
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Ratio:
A ratio is a comparison of two numbers that expresses their relative sizes. It can be written in a few different ways:
- As a fraction: a / b, where a and b are any two numbers (except b cannot be zero).
- With a colon separating the two numbers: a : b.
- As a phrase: “a to b”.
For example, the ratio of 3 to 5 can be written as 3 / 5, 3 : 5, or “3 to 5”. This means that there are 3 parts in every 5 parts, or that 3 is 60% of 5.
Proportion:
A proportion is a statement that two ratios are equivalent. It can be written in a few different ways:
- With two ratios separated by an equal sign: a / b = c / d.
- With four numbers separated by colons: a : b :: c : d.
For example, the proportion 3 / 5 = 6 / 10 means that the ratio of 3 to 5 is the same as the ratio of 6 to 10. In other words, the relationship between 3 and 5 is the same as the relationship between 6 and 10.
Properties of ratios and proportions:
- The product of the means is equal to the product of the extremes: a x d = b x c.
- The ratio of two sums is equal to the sum of the ratios: (a + b) / (c + d) = a / c + b / d.
- The ratio of two differences is equal to the difference of the ratios: (a – b) / (c – d) = a / c – b / d.
Applications of ratios and proportions:
Ratios and proportions have numerous applications in various fields, including:
- Mixing: Ratios are used to mix ingredients in recipes, chemicals in solutions, and paints in different shades.
- Scaling: Ratios are used to scale up or down drawings, maps, and models.
- Similar figures: Ratios are used to determine if two shapes are similar and to find corresponding side lengths and areas.
- Rates and percents: Ratios are used to calculate rates (such as speed, density, and interest rates) and convert between ratios and percentages.
Ratios and proportions are essential mathematical concepts with widespread applications in various fields. Understanding these concepts is crucial for solving problems in mathematics and its many real-world applications.
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Categories: Math
