Question

You have a budget of Rs. 4000 and would like to purchase LPG cylinders from a local seller who charges Rs. 50 per cylinder. The seller has a subsidy scheme by which if you return the empty cylinder purchased from him, you will get a refund of Rs. 20 per cylinder. You cannot borrow money from anyone. The maximum number of cylinders you can purchase is

• A. 131
• B. 132
• C. 133
• D. 134

Hint:

This is a refund-based iterative problem — always reduce the net cost per unit and iterate using the refunded amount until it becomes insufficient for another purchase.

Answer 1

The Correct Option is B

Step 1: Effective cost per cylinder.
Each cylinder costs Rs. 50, but returning the empty one gives Rs. 20 refund. So, the effective cost per cylinder = Rs. $50 - 20 = 30$.
Step 2: First purchase.
With Rs. 4000, you can initially buy $\frac{4000}{50} = 80$ cylinders. After using them, you return 80 empty cylinders and receive Rs. $80 \times 20 = 1600$ refund.
Step 3: Use the refund.
You can buy $\frac{1600}{50} = 32$ more cylinders, and then get Rs. $32 \times 20 = 640$ refund. With Rs. 640, you can buy $\frac{640}{50} = 12$ more cylinders, and then get Rs. $12 \times 20 = 240$ refund. With Rs. 240, you can buy $\frac{240}{50} = 4$ more cylinders, and then get Rs. $4 \times 20 = 80$ refund. Finally, with Rs. 80, you can buy $\frac{80}{50} = 1$ more cylinder.
Step 4: Total cylinders.
Total = $80 + 32 + 12 + 4 + 1 + 4$ (refund cycles) $= 133$ cylinders.
Step 5: Conclusion.
Thus, the maximum number of cylinders that can be purchased is 133.