A boat takes 10 hours to go 44 km downstream and 30 km upstream. Again, the same boat takes 13 hours to go 55 km downstream and 40 km upstream. The speed of the boat and the current will be :

1. speed of boat = 3 kmph, speed of current = 2 kmph

2. speed of boat = 6 kmph, speed of current = 4 kmph

3. speed of boat = 9 kmph, speed of current = 2 kmph

4. speed of boat = 8 kmph, speed of current = 3 kmph

42 mangoes are to be distributed among some boys and girls. If each boy is given 3 mangoes, then each girl gets 6 mangoes; and if each boy gets 5 mangoes, then each girl gets 3 mangoes. The number of boys and girls will be :

1. boys = 4, girls = 6

2. boys = 6, girls = 4

3. boys = 7, girls = 3

4. boys = 3, girls = 7

Case Study I Ritesh bought a new well-furnished two-bedroom flat in a society. The layout of the flat is shown in the figure alongside. The builder claims that the areas of the two bedrooms and the kitchen together is 95 square metres. All the dimensions in the figure are in metre (m).

Study the above information and answer the following questions.

1. Which of the following pair of linear equations represent the given situation?
   (a) x + y = 19, 2x + y = 13
   (b) x + y = 13, 2x + y = 19
   (c) x − y = 19, 2x − y = 13
   (d) x + y = 13, 2x − y = 19

2. The perimeter of the outer boundary of the layout is:
   (a) 54 m
   (b) 27 m
   (c) 50 m
   (d) 52 m

3. Total area of bedroom 1 and kitchen is:
   (a) 60 m²
   (b) 70 m²
   (c) 65 m²
   (d) 95 m²

4. The area of the living room is:
   (a) 50 m²
   (b) 60 m²
   (c) 70 m²
   (d) 75 m²

5. The cost of laying tiles on the floor of the kitchen at the rate of ₹200 per sq m is:
   (a) ₹ 7,000
   (b) ₹ 6,000
   (c) ₹ 5,200
   (d) ₹ 5,000

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