Pair of Linear Equation in Two Variables Test - 2

17x + 68y = 5 -------(1)
102x + 340y = 166 ------(2)
Multiplying equation (1) by 6, we get
102x + 408y = 30 -------(3)
Subtracting equation (2) from (3),
68y = -136
y = -2
Using the value of y in equation (1),
17x + 68(-2) = 5
17x = 141
34x = 141 × 2 = 282
34x + y = 282 - 2 = 280

Let the tens digit be x and units digit be y.
Then, (10x + y) - (10y + x) = 45
⇒ 10x + y – 10y - x = 45
⇒ 9x – 9y = 45
⇒ 9 (x – y) = 45
⇒ x – y = 5

According to the question,
17p + 136e = 197
Multiplying the whole equation by 0.5:
8.5p + 68e = 98.5

Let the cost of 1 bottle of lemonade = x
Cost of 1 packet of crisps = y
As given, 2x + y = 140 ..(i)
x + 3y = 170 ..(ii)

Multiply (ii) by (-2) and add with (i),
2x + y = 140
-2x - 6y = -340
-5y = -200
y = 40

Substitute the value of y in (ii).
x + 3(40) = 170
x + 120 = 170
x = 50
x = Rs. 50, y = Rs. 40

Let the fixed charges of the cab = Rs. x
Additional charges per km = y
According to the question,
x + 9y = 118 ..........(i)
x + 16y = 202 ............(ii)
From eq (i), we get
x = 118 – 9y ..............(iii)

Substituting this in equation (ii), we get
118 – 9y + 16y = 202
7y = 84
y = 12 ..........(iv)

Thus, putting it in eq (i), we get
x + 9(12) = 118
⇒ x + 108 = 118
⇒ x = 10
Thus, fixed charges = Rs. 10

Let the number of right answers = x
Number of wrong answers = y
According to the question,
4x – y = 100 ...........(i)
4x – 2y = 80 ...........(ii)
Thus, from eq (i), we get
y = 4x – 100

Putting this in eq (ii), we get
4x – 2(4x – 100) = 80
4x – 8x + 200 = 80
120 = 4x
⇒ x = 30

Then, substituting back this in eq (i)
4(30) – y = 100
120 – y = 100
⇒ y = 20
Thus, total questions in the test = x + y = 30 + 20 = 50

Let the speed of boat in still water = x km/h
Speed of stream = y km/hr
As we know,
Speed while rowing upstream = (x – y) km/h
Speed while rowing downstream = (x + y) km/h

Thus,
3(x + y) = 30
⇒ x + y = 10 ..............(i)
Similarly,
4(x – y) = 8
x – y = 2 ............(ii)

Now, adding (i) and (ii), we get
2x = 12
x = 6