If 16% of an electricity bill is deducted as a discount and Rs 1806 is still payable, what was the original bill amount in rupees?

Introduction / Context:
This is a classic percentage and discount question from aptitude tests. It models a real electricity bill situation where a certain percentage is deducted as a rebate or concession, and we must recover the original bill amount from the net amount paid.

Given Data / Assumptions:

• Let the original bill amount be B rupees.
• Discount given is 16% of B.
• After the discount, the payable amount is Rs 1806.
• We assume all amounts are in rupees and the percentage is applied on the full bill.

Concept / Approach:
If a discount of d% is given, the customer pays (100 - d)% of the original amount. Here the customer pays 84% of the bill, because 100% - 16% = 84%. Therefore, 0.84 * B = 1806. We can solve this linear equation to find B.

Step-by-Step Solution:
Let B be the original electricity bill. After a 16% deduction, the payable fraction is 84% = 84 / 100 = 0.84. So, 0.84 * B = 1806. Rewrite in fraction form: (84 / 100) * B = 1806. Therefore, B = 1806 * (100 / 84). Simplify 100 / 84 = 25 / 21. So B = 1806 * 25 / 21. First compute 1806 / 21 = 86. Then multiply 86 * 25 = 2150. Hence the original bill was Rs 2150.

Verification / Alternative check:
Check by recalculating the discount: 16% of 2150 = (16 / 100) * 2150 = 0.16 * 2150 = 344. Subtract the discount from the original bill: 2150 - 344 = 1806. This matches the given payable amount, confirming the answer.

Why Other Options Are Wrong:
Rs 1557, Rs 1593, Rs 2186 and Rs 2250 all give different net amounts when 16% is deducted, not equal to 1806. For example, 16% of 2186 is 349.76, and 2186 - 349.76 is not 1806.

Common Pitfalls:
Students sometimes treat 16% as the remaining part instead of the discount, leading to equations like 0.16B = 1806 which is incorrect. Another error is rounding too early or mishandling division by 84. Keeping the fraction form and simplifying step by step usually reduces mistakes.

Final Answer:
The original electricity bill was Rs 2150.