Two spices priced at ₹80 per kg and ₹160 per kg are blended. They are sold at ₹140 per kg, achieving a profit margin of 25%. What is the ratio of the two spices in the mixture?

Correct Answer: 3:2

Step-by-Step Explanation:

Step 1: Calculate the Cost Price (CP) of the mixture per kg

We are given that the selling price (SP) of the mixture is ₹140 per kg and the profit margin is 25%.

The relationship between Selling Price (SP) and Cost Price (CP) when there is a profit is given by:

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

Substituting the given values into the formula:

$140=\text{CP}\times \left(1+\frac{25}{100}\right)$

$140=\text{CP}\times \frac{125}{100}$

$140=\text{CP}\times \frac{5}{4}$

Now, solve for CP:

$\text{CP}=\frac{140\times 4}{5}$

$\text{CP}=28\times 4=112$

So, the Cost Price of the blended spice mixture is ₹112 per kg.

Step 2: Use the Rule of Alligation to find the ratio

According to the rule of alligation:

Price of cheaper spice = ₹80 per kg

Price of dearer spice = ₹160 per kg

Mean price (CP of mixture) = ₹112 per kg

We calculate the differences:

• Difference between price of dearer spice and mean price = 160 - 112 = 48

• Difference between mean price and price of cheaper spice = 112 - 80 = 32

The ratio of Cheaper spice to Dearer spice is:

$\text{Ratio}=\frac{\text{Dearer Price}-\text{Mean Price}}{\text{Mean Price}-\text{Cheaper Price}}$

$\text{Ratio}=\frac{48}{32}$

Simplifying the fraction by dividing numerator and denominator by 16:

$\text{Ratio}=\frac{3}{2}$

Thus, the ratio of the two spices in the mixture is 3:2.