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 :
Answer & explanation
Correct answer: option 1
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)]