Bananas for Rs. 120 Calculation

This problem requires calculating the total number of bananas obtained for a fixed amount, considering factors like extra items and the vendor's loss per dozen based on the original price.

Key Information Summary

• Total Cost: Rs. 120
• Extra Bananas Provided: 2
• Vendor's Loss per Dozen: Rs. 10 (relative to the original price structure)
• Objective: Determine the total number of bananas received.

Step-by-Step Calculation

1. Define Variable: Let $ N $ represent the original quantity of bananas bought for Rs. 120.
2. Original Price per Dozen: The initial price per dozen bananas was $ \frac{12 \times 120}{N} = \frac{1440}{N} $ Rupees.
3. Effective Price per Dozen: With the 2 extra bananas, the total quantity becomes $ N + 2 $. The effective price per dozen is $ \frac{12 \times 120}{N+2} = \frac{1440}{N+2} $ Rupees.
4. Formulate Loss Equation: The problem states a loss of Rs. 10 per dozen occurred compared to the original price. This translates to: $ \frac{1440}{N} - \frac{1440}{N+2} = 10 $
5. Solve for N:
   • Simplify the equation by dividing by 10: $ \frac{144}{N} - \frac{144}{N+2} = 1 $.
   • Combine terms using a common denominator: $ 144 \left( \frac{(N+2) - N}{N(N+2)} \right) = 1 $.
   • Further simplification yields: $ 144 \left( \frac{2}{N^2 + 2N} \right) = 1 $.
   • This leads to the quadratic equation: $ 288 = N^2 + 2N $, or $ N^2 + 2N - 288 = 0 $.
   • Factoring the quadratic gives: $ (N+18)(N-16) = 0 $.
   • The possible solutions are $ N = -18 $ or $ N = 16 $. Since the number of bananas must be positive, $ N = 16 $.
6. Calculate Total Bananas Received: The original quantity was $ N = 16 $ bananas. Including the 2 extra bananas, the total received is: Total Bananas = $ N + 2 = 16 + 2 = 18 $.

Final Answer Derivation

Based on the calculations, the total number of bananas received for Rs. 120 is 18.