Sheela purchases two varieties of apples – A and B – for a total of Rupees 2800. The weights in kg of A and B purchased by Sheela are in the ratio 5 : 8 but the cost per kg of A is 20% more than that of b. Sheela sells A and B with profits of 15% and 10% respectively. What is the overall profit in Rupees?
- 340
- 600
- 480
- 240
- 380
The Correct Option is A
Solution and Explanation
Let's solve the problem step by step:
Step 1: Determine the weights of A and B.
Let the weights of apples A and B be 5x and 8x respectively, based on their ratio of 5:8.
Step 2: Understand the cost per kg relationship.
Let the cost per kg of apple B be Rs y. Therefore, the cost per kg of apple A will be Rs 1.2y (20% more than B).
Step 3: Formulate the equation based on total cost.
5x * 1.2y + 8x * y = 2800
Therefore, 6xy + 8xy = 2800
So, 14xy = 2800
Thus, xy = 200
Step 4: Calculate the profit Sheela earns from each type of apple.
Sheela earns a 15% profit on A and a 10% profit on B. Calculating the selling prices:
- Selling price of A = 5x * 1.2y * 1.15
- Selling price of B = 8x * y * 1.1
Add the selling prices to find the total selling price:
Total selling price = 5x * 1.2y * 1.15 + 8x * y * 1.1
Total selling price = 5x * 1.38y + 8x * 1.1y
Total selling price = 6.9xy + 8.8xy
Total selling price = 15.7xy
Given xy = 200, the total selling price is 15.7 * 200 = 3140.
Step 5: Determine the overall profit.
Overall profit = Total selling price - Total cost price
Overall profit = 3140 - 2800 = 340
Conclusion: The overall profit is Rs 340.
Top Questions on Ratio and Proportion
Health insurance plays a vital role in ensuring financial protection and access to quality healthcare. In India, however, the extent and nature of health insurance coverage vary significantly between urban and rural areas. While urban populations often have better access to organized insurance schemes, employer-provided coverage, and awareness about health policies, rural populations face challenges such as limited outreach of insurance schemes, inadequate infrastructure, and lower awareness levels. This urban-rural divide in health insurance coverage highlights the broader issue of healthcare inequality, making it essential to analyze the factors contributing to this gap and explore strategies for more inclusive health protection. A state-level health survey was conducted.
The survey covered 1,80,000 adults across urban and rural areas. Urban residents formed 55% of the sample (that is, 99,000 people) while rural residents made up 45% (that is, 81,000 people). In each area, coverage was classified under four heads – Public schemes, Private insurance, Employer-provided coverage, and Uninsured. In urban areas, Public coverage accounted for 28% of the urban population, Private for 22%, Employer for 18%, and the remaining 32% were Uninsured. In rural areas, where formal coverage is generally lower, Public coverage stood at 35%, Private at 10%, Employer at 8%, while 47% were Uninsured.
For this survey, “Insured” includes everyone covered by Public + Private + Employer schemes, and “Uninsured” indicates those with no coverage at all. Officials noted that public schemes remain the backbone of rural coverage, while employer and private plans are relatively more prevalent in urban centres. (250 words)
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