Navneet is a bananawallah who buys a gross of bananas at Rs 10 a dozen...
Given:
- Navneet buys a gross of bananas (i.e. 12 x 144 = 1728 bananas) at Rs 10 a dozen.
- During transport and storage, 2 dozen bananas get spoilt.
- Navneet spends 10% of his outlay on transport costs.
- Navneet wants an overall profit of 20%.
To find:
- Price at which Navneet must sell a dozen bananas.
Solution:
1. Cost Price (CP) of a gross of bananas:
- Navneet buys a gross of bananas at Rs 10 a dozen.
- So, the CP of a gross of bananas = 10 x 12 x 12 = Rs 1440.
2. Transportation Cost:
- Navneet spends 10% of his outlay on transportation costs.
- Outlay = CP + Transportation Cost.
- So, Transportation Cost = 10% of (CP) = 0.1CP = 0.1 x 1440 = Rs 144.
3. Selling Price (SP) of good bananas:
- Number of good bananas = Total bananas - Spoilt bananas = 1728 - 2 x 12 = 1704.
- Let SP of each banana be x.
- SP of 12 bananas (i.e. 1 dozen) = 12x.
- Total SP of 1704 bananas = 1704x.
- Profit = SP - CP.
- Navneet wants an overall profit of 20%.
- So, Profit = 20% of CP = 0.2CP = 0.2 x 1440 = Rs 288.
- Therefore, 1704x - CP = 288.
- Substituting CP and Transportation Cost values, we get 1704x - 1440 - 144 = 288.
- Simplifying, we get 1704x = 1872.
- Therefore, x = 1872/1704 = Rs 1.10.
- So, SP of 12 bananas (i.e. 1 dozen) = 12x = 12 x 1.10 = Rs 13.20.
4. Selling Price (SP) of all bananas:
- Total SP of 1728 bananas = SP of good bananas + SP of spoilt bananas.
- SP of good bananas = 1704x = 1704 x 1.10 = Rs 1874.40.
- SP of spoilt bananas = 24 x x = 24 x 1.10 = Rs 26.40.
- Total SP of 1728 bananas = SP of good bananas + SP of spoilt bananas = Rs 1874.40 + Rs 26.40 = Rs 1900.80.
5. Price at which Navneet must sell a dozen bananas:
- To find the price at which Navneet must sell a dozen bananas, divide the total SP of all bananas by the total number of dozens of bananas (i.e. 1728/12 = 144).
- Price at which Navneet must sell a dozen bananas = Total SP of all bananas / Total number of dozens of bananas = Rs 1900.80 / 144 = Rs 13.20.
- Therefore, the answer is option (b) Rs 15.84 (since Navneet sells each banana for Rs 13.
Navneet is a bananawallah who buys a gross of bananas at Rs 10 a dozen...
A