Question

A dealer buys three kinds of dry fruits at ₹ 100, ₹ 80 and ₹ 60 per kg in the weight ratio $12:15:20$. Selling the first two together gives him $20\%$ profit; overall he has no gain no loss. Find the percentage loss on the third kind.

• A. $40\%$
• B. $20\%$
• C. $30\%$
• D. $50\%$

Hint:

Pick convenient weights to honor the ratio. Here, it made each kind's cost equal—making the overall and partial profit/loss arithmetic quick.

Answer 1

The Correct Option is A

Step 1: Compute individual costs.
Take the weights as $12,15,20$ kg.
Cost$_1=12\times 100=₹ 1200$, Cost$_2=15\times 80=₹ 1200$, Cost$_3=20\times 60=₹ 1200$.
$\Rightarrow Total \, cost =₹ 3600 (each \, kind \, costs \, ₹ 1200). $

Step 2: Selling price of first two.
Cost of first two $=₹ (1200+1200)=₹ 2400$.
Given profit $=20\%$ on these, so SP$_{12}=1.2\times 2400=₹ 2880$.

Step 3: Use overall no-profit-no-loss.
Overall SP $=$ Total cost $=₹ 3600$.
$\Rightarrow SP \, of \, third =₹ 3600-₹ 2880=₹ 720. $

Step 4: Loss% on third.
Loss $=₹ (1200-720)=₹ 480$.
Loss % $=\dfrac{480}{1200}\times 100=40\%$.
$\Rightarrow \boxed{40\%}.$