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 1000 as
hostel charges whereas a student B, who takes food for 26 days,
pays Rs 1180 as hostel charges. Find the fixed charges and the
cost of food per day.
(ii)A fraction becomeswhen 1 is subtracted
from the numerator and it becomeswhen 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 1 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 hours. If
they travel towards each other, they meet in 1 hour. What are the
speeds of the two cars?
(v)The area of a rectangle gets reduced by 9 square units, if its
length is reduced by 5 units and breadth is increased by 3 units.
If we increase the length by 3 units and the breadth by 2 units,
the area increases by 67 square units. Find the dimensions of the
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