Problem Analysis:

The question asks us to find the amount Anubhav spent on electricity bills, given the percentages spent on different items (electricity, rent, shopping) and a specific value related to the remaining income.

• Electricity: 14%
• Rent: 28%
• Shopping: 18%
• $\frac{1}{4}$ of the remaining amount = ₹5120

Calculate Total Percentage Spent

First, find the total percentage of income Anubhav spent on the mentioned items:

Total Spent Percentage = % Electricity + % Rent + % Shopping

Total Spent Percentage = \(14\% + 28\% + 18\%\)

Total Spent Percentage = \(60\%\)

Calculate Remaining Percentage

Next, calculate the percentage of income remaining:

Remaining Percentage = \(100\% - \text{Total Spent Percentage}\)

Remaining Percentage = \(100\% - 60\%\)

Remaining Percentage = \(40\%\)

Determine Income Proportion for Given Amount

We are told that $\frac{1}{4}$ of the remaining amount is ₹5120. The remaining amount represents 40% of the total income. Therefore:

\(\frac{1}{4} \times 40\% \times \text{Total Income} = ₹5120\)

\(10\% \times \text{Total Income} = ₹5120\)

Calculate Electricity Bill Spending

We need to find the amount spent on electricity, which is 14% of the total income.

We know that 10% of the income is ₹5120.

So, 1% of the income = \(\frac{₹5120}{10} = ₹512\)

Now, calculate the spending on electricity (14%):

Electricity Spending = \(14 \times (1\% \text{ of Income})\)

Electricity Spending = \(14 \times ₹512\)

Electricity Spending = \(₹7168\)

Answer: Anubhav spent ₹7168 on electricity bills.