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A telecommunication company came up with two plans- plan A and plan B for its customers. The plans are represented by linear equations where '$t$' represents the time (in minutes) bought and '$C$' represents the cost. The equations are :
Plan A : $3C = 20t$
Plan B : $3C = 10t + 300$
Based on above information, answer the following questions :
(i) If you purchase plan B, how much initial amount you have to pay ?
(ii) Charu purchased plan A. How many minutes she bought for ₹250 ?
(iii) (a) At how many minutes, do both the plans charge the same amount? What is that amount?
OR
(iii) (b) Which plan is better if you want to buy $60$ minutes? Give reason for your answer.
Plan A : $3C = 20t$
Plan B : $3C = 10t + 300$
Based on above information, answer the following questions :
(i) If you purchase plan B, how much initial amount you have to pay ?
(ii) Charu purchased plan A. How many minutes she bought for ₹250 ?
(iii) (a) At how many minutes, do both the plans charge the same amount? What is that amount?
OR
(iii) (b) Which plan is better if you want to buy $60$ minutes? Give reason for your answer.
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Solution: (i) At $t = 0, 3C = 300 \Rightarrow C = 100$
₹100 have to be paid initially. [1 mark]
(ii) $3 \times 250 = 20t \Rightarrow t = 37.5$ minutes [1 mark]
(iii) (a) $20t = 10t + 300 \Rightarrow t = 30$
Both plans charge same amount if a person buys $30$ minutes. [1 mark]
Amount $= \frac{20 \times 30}{3} = \text{Rs} 200$ [1 mark]
OR
(iii) (b) At $t = 60$, cost under plan A $= \text{Rs} 400$ [1/2 mark]
At $t = 60$, cost under plan B $= \text{Rs} 300$ [1/2 mark]
Plan B is better as ₹100 are saved. [1 mark]
₹100 have to be paid initially. [1 mark]
(ii) $3 \times 250 = 20t \Rightarrow t = 37.5$ minutes [1 mark]
(iii) (a) $20t = 10t + 300 \Rightarrow t = 30$
Both plans charge same amount if a person buys $30$ minutes. [1 mark]
Amount $= \frac{20 \times 30}{3} = \text{Rs} 200$ [1 mark]
OR
(iii) (b) At $t = 60$, cost under plan A $= \text{Rs} 400$ [1/2 mark]
At $t = 60$, cost under plan B $= \text{Rs} 300$ [1/2 mark]
Plan B is better as ₹100 are saved. [1 mark]