A tea seller mixes three qualities of tea T_{ | vedclass

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(D) First,find the cost price $(CP)$ of the initial mixture of $T_{1}, T_{2}$,and $T_{3}$ in the ratio $1:2:4$:$CP_{mix} = \frac{(1 	imes 74) + (2

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$4$

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(D) First,find the cost price $(CP)$ of the initial mixture of $T_{1}, T_{2}$,and $T_{3}$ in the ratio $1:2:4$:$CP_{mix} = \frac{(1 	imes 74) + (2 	imes 68) + (4 	imes 63)}{1+2+4} = \frac{74 + 136 + 252}{7} = \frac{462}{7} = Rs. 66$ per kg.Now,the seller adds $z$ kg of $T_{1}$ (priced at $Rs. 74$ per kg) to $4$ kg of the initial mixture (priced at $Rs. 66$ per kg).The selling price of the new mixture is $Rs. 84$ per kg with a profit of $20\%$.Therefore,the cost price of the new mixture is $CP_{new} = 84 	imes \frac{100}{120} = Rs. 70$ per kg.Using the alligation method for the new mixture:Quantity of $T_{1}$ ($z$ kg) at $Rs. 74$ per kg and quantity of initial mixture ($4$ kg) at $Rs. 66$ per kg result in a mixture at $Rs. 70$ per kg.$\frac{74 - 70}{70 - 66} = \frac{4}{z}$$\frac{4}{4} = \frac{4}{z}$$1 = \frac{4}{z} \Rightarrow z = 4$ kg.

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