The average rainfall in a city for the first four days was recorded to be 0.40 inch. The rainfall on the last two days was in the ratio of 4 : 3. The average of six days was 0.50 inch. What was the rainfall on the fifth day?

Correct Option (3)

The total rainfall for the first four days can be calculated as follows:

• Average rainfall for the first four days = 0.40 inch
• Total rainfall for the first four days = 4 days × 0.40 inch/day = 1.6 inch

The total rainfall for all six days is determined by the overall average:

• Average rainfall for six days = 0.50 inch
• Total rainfall for six days = 6 days × 0.50 inch/day = 3.0 inch

The combined rainfall for the fifth and sixth days is the difference between the total six-day rainfall and the total four-day rainfall:

• Rainfall on fifth day + Rainfall on sixth day = 3.0 inch - 1.6 inch = 1.4 inch

Given that the rainfall on the last two days was in the ratio of 4 : 3, let the rainfall on the fifth day be 4k and on the sixth day be 3k.

• 4k + 3k = 1.4 inch
• 7k = 1.4 inch
• k = 1.4 / 7 = 0.2 inch

Therefore, the rainfall on the fifth day was:

• Rainfall on fifth day = 4k = 4 × 0.2 inch = 0.8 inch

Incorrect Options:

Options 1 (0.60 inch), 2 (0.70 inch), and 4 (0.90 inch) are incorrect. These values do not align with the derived rainfall on the fifth day, which is calculated to be 0.8 inch based on the provided average rainfall data and the given ratio for the last two days. The calculation for the fifth day's rainfall leads to a unique value of 0.8 inch, making other options inconsistent with the problem's conditions.