Suvarna had purchased 1g gold at ₹15k (short for ₹15,000). This is shown by point O denoting the average price of gold that she possesses. Six different scenarios are given below for her next transaction. For each scenario estimate and mark the average price of gold she will have after the transaction.

1. (i) Purchase 1g gold at ₹30k
2. (ii) Purchase 2g gold at ₹30k
3. (iii) Purchase 1g gold at ₹10k
4. (iv) Purchase 10g gold at ₹10k
5. (v) Purchase 0.5g gold at ₹30k
6. (vi) Purchase 0.5g gold at ₹15k

Step-by-step solution

Idea: New average = 1 × 15 + (grams bought) × (price)1 + grams bought. The new point lies between O (15) and the new price, closer to whichever side has more grams.

Check: Each answer lies between 15 and the new price ✓; the more grams bought, the closer to the new price ((ii) closer to 30 than (i); (iv) closer to 10 than (iii)) ✓.

Answer to write in the exam

Common mistakes that cost marks

• Taking the midpoint every time. Only when equal amounts are bought is the new average midway.
• In (vi), thinking any purchase changes the average. Buying at the average price leaves it unchanged.
• In (v), dividing by 2 instead of 1 + 0.5 = 1.5 grams.

How this can come in the exam

Try one yourself

Suvarna has 1 g of gold at ₹15k. She buys 3 g at ₹11k. Find her new average price.

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