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?
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?
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When average itself contains an unknown quantity, form an equation using
\[
\text{Average}=\frac{\text{Total Sum}}{\text{Number of Terms}}.
\]
Updated On: Jun 11, 2026
- ₹1000
- ₹1200
- ₹1300
- ₹1400
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The Correct Option is D
Solution and Explanation
Concept:
Let the tenth person's contribution be \(x\).
The average contribution depends on the total amount contributed by all ten people.
Step 1: Calculate total contribution. Nine people contribute \[ 9\times400=3600 \] Total contribution \[ =3600+x \] Hence average contribution is \[ \frac{3600+x}{10} \]
Step 2: Use the given condition. The tenth person contributes ₹900 more than the average. Thus, \[ x=\frac{3600+x}{10}+900 \]
Step 3: Solve the equation. Multiplying by 10, \[ 10x=3600+x+9000 \] \[ 10x=12600+x \] \[ 9x=12600 \] \[ x=1400 \] Hence, \[ \boxed{\text{Tenth contribution}=₹1400} \] Therefore, \[ \boxed{\text{Answer = (D)}} \]
Step 1: Calculate total contribution. Nine people contribute \[ 9\times400=3600 \] Total contribution \[ =3600+x \] Hence average contribution is \[ \frac{3600+x}{10} \]
Step 2: Use the given condition. The tenth person contributes ₹900 more than the average. Thus, \[ x=\frac{3600+x}{10}+900 \]
Step 3: Solve the equation. Multiplying by 10, \[ 10x=3600+x+9000 \] \[ 10x=12600+x \] \[ 9x=12600 \] \[ x=1400 \] Hence, \[ \boxed{\text{Tenth contribution}=₹1400} \] Therefore, \[ \boxed{\text{Answer = (D)}} \]
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