Question

A shopkeeper has a total daily collection of 11,200, 10,650, 11,870 and 12,180 in 4 consecutive months. What should be the daily collection in the fifth month such that the average daily collection for 5 months become 11,050?

• A. 9350
• B. 9300
• C. 9250
• D. 9200

Answer 1

The Correct Option is A

Finding the Daily Collection for the Fifth Month

Step 1: Define the Formula 

The formula for the average collection is:

\[ \text{Average} = \frac{\text{Total Collection}}{\text{Number of Months}} \]

Step 2: Define Given Values

• Given collections for the first four months:
  • Month 1 = Rs. 11,200
  • Month 2 = Rs. 10,650
  • Month 3 = Rs. 11,870
  • Month 4 = Rs. 12,180
• Let \( x \) be the collection for the fifth month.
• Given that the average collection over 5 months is Rs. 11,050.

Step 3: Set Up the Equation

\[ \frac{11,200 + 10,650 + 11,870 + 12,180 + x}{5} = 11,050 \]

Step 4: Solve for \( x \)

First, calculate the sum of the known values:

\[ 11,200 + 10,650 + 11,870 + 12,180 = 45,900 \]

Now, substitute in the equation:

\[ \frac{45,900 + x}{5} = 11,050 \]

Multiply both sides by 5:

\[ 45,900 + x = 55,250 \]

Solve for \( x \):

\[ x = 55,250 - 45,900 \]

\[ x = 9,350 \]

Final Answer:

Thus, the daily collection in the fifth month should be Rs. 9,350 (Option A).