Practicing Success
Three pizza outlets A, B and C sell three types of pizza namely cheese pizza, veg pizza and paneer pizza. In a day, A can sell 40 cheese pizza, 30 veg pizza and 20 paneer pizza; B can sell 20 cheese pizza, 40 veg pizza and 60 paneer pizza; C can sell 60 cheese pizza, 20 veg pizza and 30 paneer pizza. If the revenue generated in a day by A is ₹6000, by B is ₹9000 and by C is ₹7000. If x denotes selling price of cheese pizza, y is selling price of veg pizza and z be the selling price of Paneer pizza then based on this information, answer the following question: |
The price of a cheese pizza is : |
₹50 ₹80 ₹500 ₹800 |
₹50 |
40x + 30y + 20z = 6000 ....(i) 20x + 40y + 60x = 9000 ....(ii) 60x + 20y + 30z = 7000 ....(iii) Eq. (i) multiply by 3 and Subtraction eq. (ii) from (i) 120x + 90y + 60z -(20x + 40y + 60x) = 18000 - 9000 120x + 90y + 60z -20x - 40y - 60x = 9000 100x + 50y = 900 10x + 5y = 900 ....(iv) Eq. (iii) multiply by 3 and subtraction eq. (ii) from (iii) 120x + 40y + 60z -(20x + 40y + 60z) = 14000 - 9000 120x + 40y + 60z - 20x - 40y - 60z = 5000 100x = 5000 $x = \frac{5000}{100}=50$ ....(v) Putting eq. (v) in eq. (iv) 10(50) + 5y = 900 500 + 5y = 900 ⇒ 5y = 900 - 500 $y = \frac{400}{5}=80$ y = 80 ....(vi) Putting eq. (v) & (vi) in eq. (i) 40x + 30y + 20z = 6000 ⇒ 40(50) + 30(80) + 20z = 6000 2000 + 2400 + 20z = 6000 200 + 240 + 2z = 600 2z = 600 - 440 2z = 160 $z = \frac{160}{2}=80$ z = 80 ...(vii) ∴ Price for cheese pizza = Rs. 50 [from eq. (v)] |