Case Study II
There are two mobile-phone companies – P and Q, that offer different plans. Company P charges a monthly fee of ₹ 40 plus ₹ 0.5 per minute of talk time. Company Q charges a monthly service fee of ₹ 30 plus ₹ 1 per minute of talk time.

Based on this information answer the following questions:

1. The linear equation which expresses the plan of company P is :
   (a) y = 0.5x + 40
   (b) y = 40x + 0.5
   (c) y = x + 40.5
   (d) y = 40 − 0.5x

2. The linear equation which expresses the plan of company Q is:
   (a) y = 30x + 1
   (b) y = x + 30
   (c) y = x − 30
   (d) y = 30x − 1

3. How many minutes of talk time would yield equal expenditure from both companies?
   (a) 10 minutes
   (b) 15 minutes
   (c) 20 minutes
   (d) 25 minutes

4. Manisha took the plan of company P and used 400 minutes of talk time. She spent:
   (a) ₹240
   (b) ₹430
   (c) ₹220
   (d) ₹215

5. If in a month, Anurag wants to use only 300 minutes of talk time, then which company’s plan is better for him?
   (a) Company P
   (b) Company Q
   (c) Both offer the same plan
   (d) Can’t be determined

Case Study III
Tanusha went to a bank to withdraw money. She asked the cashier to give her ₹ 100 and ₹ 500 rupee notes only. The cashier agreed. Tanusha got x, ₹ 100-rupee notes and y, 500-rupee notes.

Based on this information, answer the following questions.

1. If Tanusha withdrew ₹ 15,000, then the above information can be represented by the linear equation:
   (a) x + 5y = 150
   (b) 5x + y = 150
   (c) x + 5y + 150 = 0
   (d) x + y = 150

2. If she got 54 notes in all, then the above information can be represented by the linear equation:
   (a) 100x + 500y = 54
   (b) x + y = 54
   (c) 500x + 100y = 54
   (d) 100x + y = 54

3. If Tanusha withdraws ₹16 000, then which combination of notes might she get?
   (a) ₹500 notes = 30, ₹100 notes = 20
   (b) ₹500 notes = 25, ₹100 notes = 25
   (c) ₹500 notes = 20, ₹100 notes = 30
   (d) ₹500 notes = 30, ₹100 notes = 10

4. If she gets twenty 500-rupee notes and twenty-five 100-rupee notes, then the amount she withdraws is:
   (a) ₹10,000
   (b) ₹11,000
   (c) ₹12,000
   (d) ₹12,500

5. Can Tanusha withdraw ₹10,050 under the given conditions?
   (a) yes
   (b) no
   (c) can’t say anything
   (d) none of these

Assertion(A): A pair of linear equations in two variables cannot have more than one solution.

Reason(R): If we solve a pair of linear equations in two variables, first by elimination method and then by cross multiplication method, then in some cases the two solutions so obtained may be different.

1. A is true, R is false

2. A is false, R is true

3. Both A and R are true

4. Both A and R are false