49 Kg of blended tea contains Assam and Darjeeling tea in the ratio 5 : 2. Then the quantity of Darjeeling tea is to be added to the mixture to make the ratio of Assam to Darjeeling tea 2 : 1 is:

Shortcut Trick Initial mixture 5 : 2 (Total 7 units) = 49 kg ⇒ 1 unit = 7 kg. Assam tea = 35 kg, Darjeeling tea = 14 kg. In new ratio 2 : 1, Assam tea stays constant at 35 kg. So, 2 units = 35 kg ⇒ 1 unit (new Darjeeling) = 17.5 kg. Quantity to be added = 17.5 − 14 = 3.5 kg. ∴ The correct answer is 3.5 kg. Alternate Method Given: Total mixture = 49 kg, Initial Ratio (A : D) = 5 : 2, Final Ratio (A : D) = 2 : 1. ⇒ Total initial units = 5 + 2 = 7 units ⇒ 7 units = 49 kg ⇒ 1 unit = 7 kg ⇒ Initial Assam = 5 × 7 = 35 kg ⇒ Initial Darjeeling = 2 × 7 = 14 kg ⇒ Let quantity of Darjeeling added be x kg. ⇒ New ratio of Assam to Darjeeling = 35 ÷ (14 + x) = 2 ÷ 1 ⇒ 35 = 2 × (14 + x) ⇒ 35 = 28 + 2x ⇒ 2x = 35 − 28 = 7 ⇒ x = 7 ÷ 2 = 3.5 kg ∴ The correct answer is 3.5 kg. Additional Information Constant Quantity Principle In mixture problems where only one component is added or removed, the quantity of the other component remains unchanged. Use this constant value to find the new total or the added part. Ratio Balancing Method If ratio A:B changes to C:D by adding B, make the parts of A equal in both ratios by multiplying with suitable constants: (A:B) × C and (C:D) × A. Alligation for Mixtures This method can also be solved using alligation by considering the concentration of Darjeeling tea in the original mixture (2/7), the added portion (100% or 1/1), and the final mixture (1/3).