5. Mixture and Alligation

Medium Acceptance: 54.8%

In what ratio must a grocer mix tea at Rs. 60 per kg and Rs. 65 per kg so that by selling the mixture at Rs. 68.20 per kg he may gain 10%?

🔒

Explanation Locked

Solve the problem or choose an option on the left to reveal the step-by-step interactive solver panel.

Mixture and Alligation Quantitative Aptitude

Medium

In what ratio must a grocer mix tea at Rs. 60 per kg and Rs. 65 per kg so that by selling the mixture at Rs. 68.20 per kg he may gain 10%?

Interactive Visual Explanation

Step 1 of 2

Step 1

Find the Mean Cost Price

The selling price of the mixture is Rs. 68.20/kg at a gain of 10%. We must first calculate the baseline Mean Cost Price (CP) of the mixture.

\text{Mean CP} = \frac{\text{Selling Price}}{1 + \text{Gain\%}} = \frac{68.20}{1.10} = \text{Rs. } 62\text{/kg}

Step 2

Apply Alligation Rule

Compare the cost prices of Cheaper tea ($C = 60$), Dearer tea ($D = 65$), and the Mean mixture ($M = 62$). The ratio of Cheaper to Dearer tea is given by the cross difference:

Alligation Criss-Cross Model Hover values to see subtraction pathways

Cheaper Quantity : Dearer Quantity = 3 : 2

\text{Ratio } (\text{Cheaper} : \text{Dearer}) = \frac{D - M}{M - C} = \frac{65 - 62}{62 - 60} = \frac{3}{2}

⚡

CGL Exam Speed Trick

⚡ Alligation Trick: Always convert selling price to cost price first! A common pitfall is subtracting selling price directly ($65-68.20$ is negative!). Once you have CP = 62, cross-subtract: $65 - 62 = 3$ and $62 - 60 = 2$. The ratio is instantly 3:2. Takes 10 seconds.

⚡ Speed-Run CGL Cheatsheet

Mastering these core principles will let you solve similar questions under 30 seconds.

Core Identity:

Cheaper Qty / Dearer Qty = (Dearer Price - Mean CP) / (Mean CP - Cheaper CP)

Check the interactive visualizer in the first tab to see these formulas modeled geometrically!

My Attempts

Status Language Time Taken

No attempts recorded for this question yet. Submit your answer on the left to see stats.