Question

PAIR OF LINEAR EQUATIONS IN TWO VARIABLES
WANT THE ANSWERS FOR ALL THE THREE QUESTIONS
PLSSS

1. Sum of 3 times of the numerator and 4 times of denominator of a fraction is equal to 29. And sum of the denominator and one less than numerator is equal to 7. So find the fraction.
2. The difference between the length and breadth of a rectangle is 3 cm. If we tripple the length and double the breadth then there is an increase by 84 cm in its perimeter. So find its area.
3. In an examination BHUVANCHANDRA got 75 marks. Out of 30 questions, each correct answer is given 4 marks and each wrong answer is given -1. So how many qustions were correctly answered?

Answer 1

1. Let the fraction be x/y
Given that sum of 3 times of numerator and 4 times of denominator = 29
Therefore
3x + 4y = 29 (Equation 1)

Also given that sum of the denominator and one less than the numerator = 7
x - 1 + y = 7
x + y = 8 (Equation 2)

Taking equation 1 and 2 as simultaneous equations
1(3x + 4y = 29)
3(x + y = 8)

3x + 4y = 29
3x + 3y = 24

Subtracting equation 2 from 1
3x + 4y = 29
- 3x - 3y = - 24

y = 5
x + 5 = 8
x = 3

The fraction is (x/y) = 3/5.


2. Let the length of rectangle = x cm and breadth = y cm
Given that the difference between the length and breadth = 3 cm
x - y = 3 (Equation 1)

If the length is tripled and the breadth is doubled, the perimeter increases by 84 cm.
Therefore 
2(3x + 2y) = 84
3x + 2y = 42 (Equation 2)

Taking 1 and 2 as simultaneous equations
3 (x - y = 3)
1 (3x + 2y = 42)

3x - 3y = 9
3x + 2y = 42

Subtracting 2 from 1
3x - 3y = 9
- 3x - 2y = - 42

- 5y = - 33
y = 33/5 = 6.6 cm

x - 6.6 = 3
x = 9.6 cm

Area of the rectangle = length * breadth
                                     = 9.6 * 6.6
                                     = 63.36 cm²


3. Let the number of correct answers = x and the wrong answers = y
Total questions = 3.
Therefore
x + y = 30 (Equation 1)

Each correct answer = 4 marks
Marks for x correct answers = 4x

Each wrong answer = - 1
Marks for y wrong answers = - y

Total marks = 75
Therefore
4x - y = 75 (Equation 2)

Adding equation 1 and 2
x + y = 30
4x - y = 75

5x = 105
x = 21

21 + y = 30
y = 9

Number of answers he correctly answered = 21




Hope my answer helps you.