In what ratio should Assam tea costing ₹30 per kg be mixed with Darjeeling tea costing ₹40 per kg, so that by selling the mixture at ₹40.80 per kg, there is a gain of 20%?

Shortcut Trick Convert Selling Price of mixture to Cost Price : 40.80 ÷ 1.2 = ₹34/kg . Apply Alligation between 30, 40, and 34. Ratio = (40 − 34) : (34 − 30) = 6 : 4 . Simplified Ratio = 3 : 2 . ∴ The correct answer is 3:2. Alternate Method Given: CP of Assam tea = ₹30 per kg CP of Darjeeling tea = ₹40 per kg SP of Mixture = ₹40.80 per kg Profit percentage = 20% Formula Used: CP = [SP × 100] ÷ [100 + Profit %] Ratio = (Higher CP − Mean CP) : (Mean CP − Lower CP) Assam (30) Darjeeling (40) 34 40-34 = 6 34-30 = 4 Ratio = 6 : 4 = 3 : 2 Calculations: ⇒ Cost Price of mixture = [40.80 × 100] ÷ 120 ⇒ Cost Price of mixture = 4080 ÷ 120 = ₹34 ⇒ Quantity of Assam tea : Quantity of Darjeeling tea = (40 − 34) : (34 − 30) ⇒ Ratio = 6 : 4 ⇒ Ratio = 3 : 2 ∴ The correct answer is 3:2. Additional Information Rule of Alligation It is used to find the ratio in which two ingredients at given prices must be mixed to produce a mixture of a specific mean price. Ratio = (Price of Dearer − Mean Price) : (Mean Price − Price of Cheaper). Unit Consistency in Alligation All three values used in the alligation cross (cheaper, dearer, and mean) must be in the same unit. If prices are given, all must be either Cost Price (CP) or Selling Price (SP) at the same profit/loss condition. Profit and CP Relation If there is a gain of G%, then SP = CP × (100 + G)/100. Conversely, CP = SP × 100 / (100 + G).