Rick bought cold drinks of Rs. 56000. Then he sold 1/3rd of the total purchase to a 40% loss. How much profit does he need to ear…

Question

Rick bought cold drinks of Rs. 56000. Then he sold 1/3rd of the total purchase to a 40% loss. How much profit does he need to earn on the remaining cold drinks to cover the loss?

1. A. 20% (Correct answer)
2. B. 18%
3. C. 17%
4. D. 22%

Correct Answer

Option A — 20%

Detailed Solution & Explanation

The correct answer is 20%.

Key Points

• Total purchase: Rs. 56,000.
• Portion sold at a loss: $\frac{1}{3}$ of 56,000 $= \dfrac{56000}{3}$, sold at a 40% loss.
  • $\text{Loss} = 0.40 \times \frac{56000}{3} = \frac{22400}{3}$
• Remaining stock: $\frac{2}{3}$ of 56,000 $= \dfrac{112000}{3}$ at cost.
• To cover the loss, the profit earned on the remainder must equal $\dfrac{22400}{3}$:
  • $\text{Required profit}\% = \frac{22400/3}{112000/3} \times 100 = \frac{22400}{112000} \times 100 = \mathbf{20\%}$

Shortcut Trick

• The thirds cancel, so the actual rupee amounts never matter:
  • Loss on $\frac{1}{3}$ at 40% $= \frac{1}{3} \times 0.4 = \frac{0.4}{3}$ of the total cost.
  • Required profit on $\frac{2}{3}$ $= \frac{0.4}{3} \div \frac{2}{3} = \frac{0.4}{2} = 0.20 = \mathbf{20\%}$
• General rule: if a fraction $f$ is sold at a loss of $L\%$, the remaining $(1-f)$ must earn $\dfrac{f \times L}{1 - f}$ per cent to break even.

Alternate Method

• Take convenient numbers: cost Rs. 56,000, one-third $\approx$ Rs. 18,666.67 sold for 60% of that $=$ Rs. 11,200, a loss of Rs. 7,466.67.
• Remaining cost Rs. 37,333.33 must yield a profit of Rs. 7,466.67, which is $\frac{7466.67}{37333.33} = 20\%$. ✓

Additional Information

• Note what "cover the loss" means — it means breaking even overall, not making an additional profit. Questions that ask for a *net* gain on top of covering the loss require the target profit to be added before dividing.
• Because the remaining stock is twice the quantity sold at a loss, it only needs half the percentage change to compensate — 40% loss on one part is offset by 20% gain on two parts.