A businessman blends Assam tea costing Rs.70 per kg with Darjeeling tea costing Rs.110 per kg in the ratio 3 ∶ 1. What should be the selling price per kg of the new mixture to have a profit of \(12\frac{1}{2}\) % for him? 12 1 2 " id="MathJax-Element-14-Frame" role="presentation" style="display: inline; word-spacing: 0px; position: relative;" tabindex="0"> 12 1 2 12 1 for him ?

The correct answer is option 2 Given: A businessman blends Assam tea costing Rs.70 per kg with Darjeeling tea costing Rs.110 per kg in the ratio 3 ∶ 1 Calculation: Let assume cost price of the mixture = Rs X per kg Let the proportion of Assam tea costing Rs. 70 and Darjeeling tea costing Rs. 110 in the mixture is 3c and c. ⇒ \(\dfrac{70 \times 3c + 110 \times c}{3c + c} = X\) ⇒ X = \(\dfrac{320}{4}\) ⇒ X = Rs. 80 per kg To make a profit of 12 \(\dfrac{1}{2}\) % The selling price = 112 \(\dfrac{1}{2}\) % of cost price The selling price = \(\dfrac{225}{200} \times 80\) The selling price = Rs. 90 per kg Alternate Method Let assume cost price of the mixture = Rs X per kg So, the ratio of mixture between Assam and Darjeeling tea The ratio of Assam and Darjeeling tea in the mixture is 3 : 1 ⇒ \(\dfrac{110-X}{X-70} = \dfrac{3}{1}\) ⇒ 110 - X = 3(X - 70) ⇒ 110 - X = 3X - 210 ⇒ 4X = 320 ⇒ X = 80 So, the cost price of the mixture is Rs. 80 per kg. To have a profit of 12 \(\dfrac{1}{2}\) %, the selling price = 112 \(\dfrac{1}{2}\) % of cost price = \(\dfrac{225}{200} \times 80\) = Rs. 90 per kg So, the selling price should be Rs. 90 per kg to have a profit of 12 \(\dfrac{1}{2}\) %.