A merchant mixes 50 kg of rice costing ₹60/kg with another variety costing ₹90/kg. He sells at ₹75/kg with 8% profit. How much of the second variety(approximate) did he mix?

Correct Option: 23 kg

Step-by-Step Explanation:

1. Find the overall Cost Price (CP) per kg of the mixture:

The merchant sells the mixture at a Selling Price (SP) of ₹75/kg and makes an 8% profit.

The relation between Selling Price, Cost Price, and Profit Percentage is given by:

$\text{SP}=\text{CP}\times \left(1+\frac{\text{Profit \%}}{100}\right)$

Substituting the given values into the formula:

$75=\text{CP}\times \left(1+\frac{8}{100}\right)$

$75=\text{CP}\times \frac{108}{100}$

$\text{CP}=\frac{75\times 100}{108}$

$\text{CP}=\frac{7500}{108}=\text{₹}69.44\text{per kg (approx.)}$

2. Set up the equation using total cost of ingredients:

Let the quantity of the second variety of rice be x kg.

Cost of 1st variety = 50 kg × ₹60/kg = ₹3000

Cost of 2nd variety = x kg × ₹90/kg = 90x

Total weight of mixture = (50 + x) kg

Total cost of mixture = Mean CP × Total weight

$3000+90x=\frac{7500}{108}\times (50+x)$

Multiply both sides by 108 to clear the fraction:

$108\times (3000+90x)=7500\times (50+x)$

3. Solve for x:

$9720x-7500x=375000-324000$

$2220x=51000$

$x=\frac{51000}{2220}$

$x\approx 22.97\text{kg}$

Rounding to the nearest whole number gives 23 kg.