Difficulty: Medium
Correct Answer: 20
Explanation:
Introduction / Context:
This question combines ratio, unitary method and percentage spending. Manisha can use a fixed amount either to buy a certain number of Chocobars or a certain number of Fivestar chocolates, which implies a relationship between their individual prices. After spending part of the money on petrol, she buys a combination of the two types of chocolates. The task is to determine how many Chocobars she can purchase with the remaining amount.
Given Data / Assumptions:
Concept / Approach:
Let the price of one Chocobar be C and the price of one Fivestar be F. From the initial information, total amount A equals 50C and also equals 40F. This allows us to express F in terms of C. After spending 10% on petrol, the remaining amount is 0.9A. We compute the cost of 20 Fivestars and subtract this from 0.9A to see how much money remains for Chocobars. Dividing that remainder by the price per Chocobar gives the required number of Chocobars.
Step-by-Step Solution:
Step 1: Let total amount be A rupees.
Step 2: Let price of one Chocobar = C and price of one Fivestar = F.
Step 3: From A = 50C and A = 40F, we get 50C = 40F.
Step 4: Therefore, F = (50/40)C = (5/4)C = 1.25C.
Step 5: She spends 10% of A on petrol, so remaining money = 0.9A.
Step 6: Since A = 50C, remaining money = 0.9 * 50C = 45C.
Step 7: She buys 20 Fivestars, so cost of these = 20F = 20 * 1.25C = 25C.
Step 8: Money left for Chocobars = 45C - 25C = 20C.
Step 9: Number of Chocobars she can buy = (money left) / (price per Chocobar) = 20C / C = 20.
Verification / Alternative check:
Assume specific prices for clarity: take C = Rs. 2. Then A = 50 * 2 = Rs. 100 and F = 1.25 * 2 = Rs. 2.50. After spending 10% of 100 on petrol, she has Rs. 90. Cost of 20 Fivestars = 20 * 2.50 = Rs. 50. Remaining amount = 90 - 50 = Rs. 40. Each Chocobar costs Rs. 2, so she can buy 40 / 2 = 20 Chocobars, which confirms the result.
Why Other Options Are Wrong:
If she could buy 24, 26, 28 or 22 Chocobars, the total money spent on chocolates plus petrol would no longer equal her original amount A when we use the derived price relationship F = 1.25C. A full recomputation with those quantities shows mismatched totals, making them inconsistent with the given conditions.
Common Pitfalls:
Students sometimes overlook that the same initial amount is used for both purchasing scenarios, leading to an incorrect relationship between C and F. Another common error is to apply the 10% deduction incorrectly, for example subtracting from the number of chocolates instead of the money. Carefully translating each step into algebra with the correct base amounts avoids such mistakes.
Final Answer:
Manisha can buy 20 Chocobars with the remaining money.
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