Question

A grocer mixes 40 kg of lentils costing ₹65 per kg with a certain quantity of lentils costing ₹80 per kg. If he sells the mixture at ₹75 per kg, making a 10% profit, what quantity of the second type of lentils did he mix?

• A. 25.98 kg
• B. 10.77 kg
• C. 35 kg
• D. 40 kg

Answer 1

Answer:

B. 10.77 kg

Let the quantity of lentils costing ₹80/kg be (x) kg.

Step 1: Find the cost price of the mixture per kg

The mixture is sold at ₹75/kg with a 10% profit.

$\text{Cost Price per kg of mixture}=\frac{75}{1.10}$
$=\frac{750}{11}$
$\approx 68.18$

Step 2: Use the weighted average equation

Total cost of the mixture:

$40 \times 65 + x \times 80$

Total quantity:

40 + x
Average cost price per kg:

$\frac{2600 + 80x}{40 + x}=\frac{750}{11}$

Cross-multiplying:

$11(2600+80x)=750(40+x)$
$28600+880x=30000+750x$
$130x=1400$
$x=\frac{1400}{130}=\frac{140}{13}$
x \approx 10.77$<br></p><p data-pxy="true" style="color: rgb(0,0,0); margin-top: 2px; margin-bottom: 2px;">Answer</p><p data-pxy="true" style="color: rgb(0,0,0); margin-top: 2px; margin-bottom: 2px;">$\boxed{\frac{140}{13}\text{ kg} \approx 10.77\text{ kg}}$

So, the grocer mixed about 10.77 kg of the ₹80/kg lentils.