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Form the pair of linear equations in the following problems and find their solutions (if they exist) by any algebraic method :

(i) A part of monthly hostel charges is fixed and the remaining depends on the number of days one has taken food in the mess. When a student A takes food for 20 days she has to pay Rs. 1,000 as hostel charges whereas a student B, who takes food for 26 days, pays Rs. 1,180 as hostel charges. Find the fixed charges and the cost of food per day.

(ii) A fraction becomes 1/3, when 1 is subtracted from the numerator and it becomes 1/4, when 8 is added to its denominator. Find the fraction.

(iii) Yash scored 40 marks in a test, getting 3 marks for each right answer and losing L mark for each wrong answer. Had 4 marks been awarded for each correct answer and 2 marks been deducted for each incorrect answer, then Yash would have scored 50 marks. How many questions were there in the test ?

(iv) Places A and B are 100 km apart on a highway. One car starts from A and another from B at the same time. If the cars travel in the same direction at different speeds, they meet in 5 hr. If they travel towards each other, they meet in 1 hr. What are the speeds of the two cars ?

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(i) Let fixed part of monthly hostel charges be Rs. y

Cost of food for one day be Rs. x

(iii) Let the number of right answers be x

and the number of wrong answers be y.

Total number of questions : x + y

In first case,

Marks awarded for x right answers = 3x.

Marks lost for y wrong answers = y x 1 = y

(iv) Let speed of car I be x km/hr

and speed of car II be y km/hr

Car I starts from point A and car II starts from point B

Hence, the speed of the two cars are respectively 50 km/hr and 40 km/hr.

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