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 Rs. 6000, by B is Rs. 9000 and by C is Rs. 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 paneer pizza is :
Answer & explanation
Correct answer: option 4
The correct answer is Option (4) → Rs. 80
The revenue of each outlet gives one equation. Dividing each by 10:
\(4x + 3y + 2z = 600 \quad \text{(i)}\)
\(2x + 4y + 6z = 900 \quad \text{(ii)}\)
\(6x + 2y + 3z = 700 \quad \text{(iii)}\)
Eliminating z, first from (i) and (ii): 3 × (i) − (ii) gives
\(12x + 9y + 6z - (2x + 4y + 6z) = 1800 - 900\)
\(10x + 5y = 900\)
\(2x + y = 180 \quad \text{(iv)}\)
Then from (ii) and (iii): (ii) − 2 × (iii) gives
\(2x + 4y + 6z - (12x + 4y + 6z) = 900 - 1400\)
\(-10x = -500\)
\(x = 50\)
From (iv):
\(y = 180 - 100 = 80\)
From (i):
\(200 + 240 + 2z = 600\)
\(2z = 160\)
\(z = 80\)
The price of a paneer pizza is Rs. 80. Check in (iii): \(300 + 160 + 240 = 700\).