A part of monthly hostel charges in a college is fixed and the remaining depends on the number of days one has taken food in the mess. When a student Anu takes food for 25 days, she has to pay Rs 4500 as hostel charges, whereas another student Bindu who takes food for 30 days, has to pay Rs 5200 as hostel charges.

Considering the fixed charges per month by Rs x and the cost of food per day by Rs y, then answer the following questions.
(i) Represent algebraically the situation faced by both Anu and Bindu.

(ii) The system of linear equations, represented by above situations has

(iii) The cost of food per day is

(iv) The fixed charges per month for the hostel is

(v) If Bindu takes food for 20 days, then what amount she has to pay?

From Bengaluru bus stand, if Riddhima buys 2 tickets to Malleswaram and 3 tickets to Yeswanthpur, then total cost is Rs 46; but if she buys 3 tickets to Malleswaram and 5 tickets to Yeswanthpur, then total cost is Rs 74.

Consider the fares from Bengaluru to Malleswaram and that to Yeswanthpur as Rs x and Rs y respectively and answer the following questions.
(i) 1^st situation can be represented algebraically as

(ii) 2^nd situation can be represented algebraically as

(iii), Fare from Ben~aluru to Malleswaram is

(iv) Fare from Bengaluru to Yeswanthpur is

(v) The system oflinear equations represented by both situations has

Points A and B representing Chandigarh and Kurukshetra respectively are almost 90 km apart from each other on the highway. A car starts from Chandigarh and another from Kurukshetra at the same time. If these cars go in the same direction, they meet in 9 hours and if these cars go in opposite direction they meet in 9/7 hours. Let X and Ybe two cars starting from points A and B respectively and their speed be x km/hr and y km/hr respectively.

Then, answer the following questions.
(i) When both cars move in the same direction, then the situation can be represented algebraically as

(ii) When both cars move in opposite direction, then the situation can be represented algebraically as

(iii) Speed of car X is

(iv) Speed of car Y is

(v) If speed of car X and car Y, each is increased by 10 km/hr, and cars are moving in opposite direction, then after how much time they will meet?

Mr Manoj Jindal arranged a lunch party for some of his friends. The expense of the lunch are partly constant and partly proportional to the number of guests. The expenses amount to Rs 650 for 7 guests and Rs 970 for 11 guests .

Denote the constant expense by Rs x and proportional expense per person by Rs y and answer the following questions.
(i) Represent both the situations algebraically.

(ii) Proportional expense for each person is

(iii) The fixed (or constant) expense for the party is

(iv) If there would be 15 guests at the lunch party, then what amount Mr Jindal has to pay?

(v) The system of linear equations representing both the situations will have

In a office, 8 men and 12 women together can finish a piece of work in 10 days, while 6 men and 8 women together can finish it in 14 days. Let one day's work of a man be l/x and one day's work of a woman be 1/y.

Based on the above information, answer the following questions.
(i) 1^st situation can be represented algebraically as

(ii) 2^nd situation can be represented algebraically as

(iii) One woman alone can finish the work in

(iv) One man alone can finish the work in

(v) If 14 men and 28 women work together, then in what time, the work will be completed?

From a shop, Sudhir bought 2 books of Mathematics and 3 books of Physics of class X for Rs 850 and Suman bought 3 books of Mathematics and 2 books of Physics of class X for Rs 900. Consider the price of one Mathematics book and that of one Physics book be Rs x and Rs y respectively.

Based on the above information, answer the following questions.
(i) Represent the situation faced by Sudhir, algebraically,

(ii) Represent the situation faced by Suman, algebraically

(iii) The price of one Physics book is

(iv) The price of one Mathematics book is

(v) The system of linear equations represented by above situation, has

A boat in the river Ganga near Rishikesh covers 24 km upstream and 36 km downstream in 6 hours while it covers 36 km upstream and 24 km downstream in \(6 \frac{1}{2}\) hours. Consider speed of the boat in still water be x km/hr and speed of the stream be y km/hr and answer the following questions.

(i) Represent the 1^st situation algebraically.

(ii) Represent the 2^nd situation algebraically.

(iii) If u \(=\frac{1}{x-y} \text { and } v=\frac{1}{x+y}, \text { then } u=\)

(iv) Speed of boat in still water is

(v) Speed of stream is

Piyush sells? saree at 8% profit and a sweater at 10% discount, thereby, getting a sum of Rs 1008. If he had sold the saree at 10% profit and the sweater at 8% discount, he would have got Rs 1028.

Denote the cost price of the saree and the list price (price before discount) of the sweater by Rs x and Rs y respectively
and answer the following questions.
(i) The 1^st situation can be represented algebraically as

(ii) The 2^nd situation can be represented algebraically as

(iii) Linear equation represented by 1^st situation intersect the x-axis at

(iv) Linear equation represented by 2^nd situation intersect the y-axis at

(v) Both linear equations represented by situation 1^st and 2^nd intersect each other at

Puneet went for shopping in the evening by metro with his father who is an expert in mathematics. He told Puneet that path of metro A is given by the equation 2x + 4y = 8 and path of metro B is given by the equation 3x + 6y = 18. His father put some questions to Puneet. Help Puneet to solve the questions.

(i) Equation 2x + 4y = 8 intersects the x-axis and y-axis respectively at

(ii) Equation 3x + 6y = 18 intersects the x-axis and y-axis respectively at

(iii) Coordinates of point of intersection of two given equations are

(iv) Represent the equations, 2x + 4y = 8 and 3x + 6y = 18 graphically.

	(d) None of these

(v) System oflinear equations represented by two given lines is

Raman usually go to a dry fruit shop with his mother. He observes the following two situations.
On 1st day: The cost of 2 kg of almonds and 1 kg of cashew was Rs 1600.
On 2nd day: The cost of 4 kg of almonds and 2 kg of cashew was Rs 3000.
Denoting the cost of 1 kg almonds by Rs x and cost of 1 kg cashew by Rs y, answer the following questions.

(i) Represent algebraically the situation of day-I.

(ii) Represent algebraically the situation of day- II.

(iii) The linear equation represented by day-I, intersect the x axis at

(iv) The linear equation represented by day-II, intersect the y-axis at

(v) Linear equations represented by day-I and day -II situations, are

In the below given layout, the design and measurements has been made such that area of two bedrooms and Kitchen together is 95 sq. m.

(i) The area of two bedrooms and kitchen are respectively equal to

(ii) Find the length of the outer boundary of the layout.

(iii) Find the area of each bedroom.

(iv) Find the area of living room in the layout.

(v) Find the cost of laying tiles in Kitchen at the rate of Rs. 50 per sq. m

On a bright Sunday morning three friends A, B and C decided to go on river for fishing and boating. They decided to leave for the place together in the evening. The journey was smooth, it just went as scheduled then they reached to the river, and started to set the boat on sail. They were enjoying their ride with full speed. They started boating from a place to another place which is at a distance of 42 km and then again returns to the starting place. They took 20 hours in all. The time taken by them riding downstream in going 14 km is equal to the time taken by them riding upstream in going 6 km.

For calculating they took speed of the boat as x km/hr and the speed of the river as y km/hr. Based on the above situation, answer the following questions:
(i) The speed of the boat in downstream is

(ii) The speed of the boat in upstream is

(iii) The speed of the boat in still water is

(iv) The speed of the river is

(v) The speed of boat in upstream is

Deepak bought 3 notebooks and 2 pens for Rs. 80. His friend Ram said that price of each notebook could be Rs. 25. Then three notebooks would cost Rs.75, the two pens would cost Rs.5 and each pen could be for Rs. 2.50. Another friend Ajay felt that Rs. 2.50 for one pen was too little. It should be at least Rs. 16. Then the price of each notebook would also be Rs.16.
      
Lohith also bought the same types of notebooks and pens as Aditya. He paid 110 for 4 notebooks and 3 pens. Later, Deepak guess the cost of one pen is Rs. 10 and Lohith guess the cost of one notebook is Rs. 30.

(i) Form the pair of linear equations in two variables from this situation by taking cost of one notebook as Rs. x and cost of one pen as Rs. y.

(ii) Find the cost of one pen?

(iii)  Find the total cost if they will purchase the same type of 15 notebooks and 12 pens.

(iv)  Find whose estimation is correct in the given statement.