Question

Ten people went out for dinner. Nine of them contributed ₹400 each, while the tenth person contributed an amount that was ₹900 more than the average contribution of the entire group. How much did the tenth person contribute?

• A. ₹1000
• B. ₹1200
• C. ₹1300
• D. ₹1400

Hint:

When average itself contains an unknown quantity, form an equation using \[ \text{Average}=\frac{\text{Total Sum}}{\text{Number of Terms}}. \]

Answer 1

The Correct Option is D

Step 1: Name the unknown.
Let the tenth person's contribution be $x$ rupees. The other nine each gave $400$.
Step 2: Write the total amount.
Nine people give $9\times 400=3600$, so the group total is $3600+x$.
Step 3: Write the average.
The average over all ten people is \[ \frac{3600+x}{10} \]
Step 4: Translate the key condition.
The tenth gave $900$ more than this average, so \[ x=\frac{3600+x}{10}+900 \]
Step 5: Clear the fraction.
Multiply through by $10$: \[ 10x=3600+x+9000 \] which gives $9x=12600$.
Step 6: Solve.
\[ x=\frac{12600}{9}=1400 \] So the tenth person contributed $1400$ rupees.
\[ \boxed{1400} \]