A company produced 1500 units at a total cost of ₹1,20,000. It donated 300 units to an NGO. For the rest, it announced a 15% discount on the market price of ₹110 per unit. It also offered 3 units free for every 10 units purchased. If all 1500 units were distributed, what is the overall gain or loss percentage?

Correct Option: 28.08% loss

Step-by-Step Explanation:

1. Understand the Total Cost Price (CP):
The company produces 1500 units at a total cost of ₹1,20,000.
So, Total Cost Price (CP) = ₹1,20,000.

2. Calculate the Remaining Units after Donation:
Units donated to NGO = 300 units.
Remaining units available for distribution/sale = 1500 - 300 = 1200 units.

3. Analyze the Selling Offer and Revenue per Deal:
The company offers 3 units free for every 10 units purchased.
This means for every purchase transaction of 10 units, a total of (10 + 3) = 13 units are handed over to the customer.
However, the customer only pays for 10 units.

4. Calculate the Discounted Selling Price per Paid Unit:
Market price per unit = ₹110.
Discount offered = 15%.
Selling price for 1 paid unit = Market Price × (100 - Discount)%
$\text{Selling price per paid unit}=110\times \left(1-0.15\right)=110\times 0.85=\text{₹}93.50$

5. Calculate the Total Revenue (Total Selling Price):
Total units distributed via sale = 1200 units.
Since units are given in groups of 13 (10 paid + 3 free):
Number of full schemes/groups = $\frac{1200}{13}$
In each group of 13 units, revenue is collected for 10 units.
So, Total Paid Units = $\frac{1200}{13}\times 10=\frac{12000}{13}$ units.

Total Revenue (Selling Price, SP) = Paid Units × Selling price per paid unit
$\text{Total SP}=\frac{12000}{13}\times 93.50=\frac{1122000}{13}\approx mo><mtext>₹</mtext><mn>86,307.69</mn>$

6. Calculate Overall Gain or Loss Percentage:
Since Total SP (₹86,307.69) is less than Total CP (₹1,20,000), there is an overall loss.
$\text{Loss}=\text{CP}-\text{SP}=120000-86307.69=\text{₹}\mathrm{33,692.31}$

$\text{Loss Percentage}=\left(\frac{\text{Loss}}{\text{Total CP}}\right)\times 100$

$\text{Loss Percentage}=\left(\frac{120000-\frac{1122000}{13}}{120000}\right)\times 100$

$\text{Loss Percentage}=\left(1-\frac{1122}{1200\times 13}\right)\times 100=\left(1-\frac{187}{260}\right)\times 100$

$\text{Loss Percentage}=\frac{73}{260}\times 100=\frac{730}{26}\approx 28.0769\%\approx 28.08\%$

Thus, the overall loss percentage is 28.08% loss.