Question

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 Plant B : 3C = 10t + 300

Based on the above information, answer the following questions:

1. If you purchase plan B, how much initial amount you have to pay?  (1)
2. Charu purchased plan A. How many minutes she bought for ₹250?  (1)
3. 1. At how many minutes, do both the plans charge the same amount? What is that amount?  (2)
      OR
   2. Which plan is better if you want to buy 60 minutes? Give reason for your answer. (2)

Answer 1

i. For plan B : 3C = 10t + 300

To find initial amount for plan B,

We put t = 0

3C = 10t + 300

⇒ 3C = 10 × 0 + 300

⇒ 3C = 0 + 300

⇒ 3C = 300

⇒ C = `300/3`

⇒ C = 100

ii. Chase purchased plan A.

∵ Plan A : 3C = 20t

C = ₹ 250

Putting the value of C in plan A.

3C = 20t

⇒ 3 × 250 = 20t

⇒ 750 = 20t

⇒ t = `750/20`

⇒ t = 37.5 minutes

iii. a. If both plan have same changes

Plan A : 3C = 20t

C = `(20t)/3`   ...(1)

Plan B : 3C = 10t + 300

⇒ C = `(10t + 300)/3`   ...(2)

From equation (1) and equation (2),

`(20t)/3 = (10t + 300)/3`

⇒ 20t = 10t + 300

⇒ 20t – 10t = 300

⇒ 10t = 300

⇒ t = `300/10`

⇒ t = 30 minutes

For amount, putting the value of t in plan A and plan B

3C = 20t

⇒ 3C = 20 × 30

⇒ 3C = 600

⇒ C = `600/3`

⇒ C = ₹ 200

3C = 10t + 30

⇒  3C = 10 × 30 + 300

⇒ 3C = 300 + 300

⇒ 3C = 600

⇒ C = `600/3`

⇒ C = ₹ 200

OR

b. For t = 60 minutes.

To find which plan is best, putting the value of t = 60 is both plan A and plan B.

Plan A : 3C = 20t

⇒ 3C = 20 × 60

⇒ 3C = 1200

⇒ C = `1200/3`

⇒ C = ₹ 400

Plan B : 3C = 10t + 300

⇒ 3C = 10 × 60 + 300

⇒ 3C = 600 + 300

⇒ 3C = 900

⇒ C = `900/3`

⇒ C = ₹ 300

∵ 400 > 300

Plan A > Plan B

So, plan B is best, because it’s low cost.