In what proportion must tea worth Rs. 27 and Rs. 31 per kg be mixed so as to gain 25% by selling the mixture at Rs. 36 per kg?

Given:

Tea worth Rs. 27 per kg and Rs. 31 per kg

Selling price of the mixture to gain 25% = Rs. 36 per kg

Concept:

We use the concept of alligation to find the ratio in which two varieties must be mixed.

Formula Used:

Alligation rule:

If two ingredients are mixed, then the ratio of the quantities of the two ingredients is given by:

⇒ (C₁ - C_m) : (C_m - C₂)

where C₁ and C₂ are the costs of the two ingredients, and C_m is the mean cost of the mixture.

Calculation:

Let the cost price of the mixture be C_m.

Given selling price of mixture = Rs. 36 per kg

Gain = 25%

⇒ Cost price of mixture (C_m) = Selling price / (1 + Gain)

⇒ C_m = 36 / (1 + 0.25)

⇒ C_m = 36 / 1.25

⇒ C_m = 28.8

Using the alligation rule:

⇒ (C₁ - C_m) : (C_m - C₂)

⇒ (31 - 28.8) : (28.8 - 27)

⇒ 2.2 : 1.8

⇒ 11 : 9

∴ The correct answer is option 4 (11 ∶ 9).