Question

A merchant has $1000$ kg of sugar, part of which he sells at $8\%$ profit and the rest at $18\%$ profit. He gains $14\%$ on the whole. The quantity of sugar sold at $18\%$ profit is

• A. $560$ kg
• B. $600$ kg
• C. $400$ kg
• D. $640$ kg

Answer 1

The correct option is B $600$ kg

Let the C.P. of sugar be Rs. $x$ per kg.
Then, C.P. $=$ Rs. 1$000x$
Let the sugar sold at $8\%$ gain by $y$ kg.
Then, sugar sold at $18\%$ gain $=(1000-y)$ kg
$\therefore (\frac{108}{100}\times xy)+[\frac{118}{100}\times x(1000-y\left)\right]=\frac{114}{100}\times 1000x$
$\Rightarrow \frac{108y}{100}+1180-\frac{118y}{100}=1140$
$\Rightarrow \frac{10y}{100}=40$

$\Rightarrow y=400$
$\therefore$ Quantity sold at 18% gain $=(1000-400)$ kg
$=600$ kg.