After a 31% deduction on an electricity bill, an amount of Rs. 1794 is still payable.\nWhat was the original bill amount before the deduction?

Introduction / Context:
This question illustrates how to reverse a percentage deduction to find the original amount. It uses a real life situation of an electricity bill that has had a certain percentage deducted, possibly as a rebate or subsidy, leaving a final payable amount. Being comfortable with reversing percentages is a valuable skill for many financial and billing problems.

Given Data / Assumptions:

• The original electricity bill is unknown and is to be found.
• There is a deduction of 31% on the original bill.
• After this deduction, the payable amount is Rs. 1794.
• All amounts are in rupees and positive.

Concept / Approach:
A deduction of 31% means that the customer pays 69% of the original bill, because 100% - 31% = 69%. Let the original bill be B. Then, 69% of B equals 1794. This gives a simple linear equation: 0.69 * B = 1794. Solving this equation yields the value of B. This is a direct reverse percentage calculation.

Step-by-Step Solution:
Step 1: Let the original bill amount be B rupees. Step 2: A 31% deduction means the customer pays 69% of B, so 69% of B = 1794. Step 3: Write this mathematically: (69 / 100) * B = 1794. Step 4: Convert to decimal: 0.69 * B = 1794. Step 5: Solve for B by dividing both sides by 0.69: B = 1794 / 0.69. Step 6: Compute B = 2600, so the original bill was Rs. 2600.

Verification / Alternative check:
Check by recalculating the deduction from the original bill of Rs. 2600. Deduction at 31% = (31 / 100) * 2600 = 806. Remaining payable amount = 2600 - 806 = 1794, which matches the given value. This confirms that our reverse percentage calculation is correct.

Why Other Options Are Wrong:
Rs. 1369 and Rs. 1405: These are much lower than 1794 and cannot yield a 69% value of 1794.
Rs. 2636: If 69% of B were 1794, B would be slightly higher than 2600 only if the percentage were slightly lower than 69; this value does not fit the equation exactly.
Rs. 2200: 69% of 2200 is 1518, not 1794, so it is clearly incorrect.

Common Pitfalls:
Some students mistakenly treat 31% as the amount paid instead of the deduction, which would lead them to set 0.31B = 1794. Others subtract 31 from 1794 or attempt to compute the difference without setting a proper equation. The safest way is to convert the verbal description into a clear percentage of the original amount and then solve.

Final Answer:
The original electricity bill amount was Rs. 2600.