Question

10 people went to a restaurant to have a meal as a group. Of these, 9 had already contributed Rs 400 each, while the 10th person had to give the entire additional amount required to honour the restaurant's bill. How much did this person pay if he had to pay Rs 900 more than the group's average?

• A. Rs 1360
• B. Rs 1350
• C. Rs 1400
• D. Rs 1300

Hint:

The 10th person pays the Average + the excess, which is the total payment.

Answer 1

The Correct Option is C

Step 1: Define the average.
Ten people split the bill. Let the group's average payment be $A$ rupees, so the total bill is $10A$.
Step 2: Add up the known contributions.
Nine people each paid 400, contributing $9 \times 400 = 3600$.
Step 3: Express the tenth person's payment.
The tenth paid 900 more than the average, that is $A + 900$.
Step 4: Write the total equation.
The two parts make up the whole bill: $3600 + (A + 900) = 10A$.
Step 5: Solve for the average.
$4500 + A = 10A$, so $4500 = 9A$ and $A = 500$.
Step 6: Find the tenth person's payment.
Tenth payment $= A + 900 = 500 + 900 = 1400$. A quick check: total is $3600 + 1400 = 5000 = 10 \times 500$, correct. So the person paid Rs 1400, matching option 3.
\[ \boxed{\text{Rs } 1400} \]