Linear Equations in One variable Test

Result

Linear Equations in One variable Test - 2

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Question 1
1 / -0

If the angles of a quadrilateral are in ratio 2 : 3 : 6 : 7, then find the difference between the largest and the smallest angles of the quadrilateral.

A
120°

B
100°

C
90°

D
80°

Solution

Let the angles of quadrilateral be 2x, 3x, 6x and 7x.
2x + 3x + 6x + 7x = 360°
18x = 360°
x = 20°

So, angles of quadrilateral = 2 x 20 = 40°
3 x 20 = 60°
6 x 20 = 120°
7 x 20 = 140°

So, the difference between the largest and the smallest angle = 140 - 40 = 100°
Question 2
1 / -0

Of the classes A and B in a school, 12% of the total students are in class A and the rest in class B. The difference between the number of students in classes A and B is 152. Find the total number of students in both the classes.

A
100

B
200

C
300

D
400

Solution

Let the total students be x.
Number of students in class A = 12% of x = 0.12x

Now, number of students in class B = x - 0.12x = 0.88x
Now, 0.88x - 0.12x = 152
0.76x = 152
x = 200
Question 3
1 / -0

Amit is 24 years older than Rohit. 2 years hence, his age will be twice the age of Rohit. Find the present age of Rohit.

A
22 years

B
21 years

C
20 years

D
19 years

Solution

Let the present age of Rohit be x.
Age of Amit = x + 24

Two years hence,
x + 24 + 2 = 2(x + 2)
x + 26 = 2x + 4
x = 22
Question 4
1 / -0

P is two years older than Q and Q is twice as old as R. If combined age of all of them is 27, then find the age of Q.

A
10 years

B
12 years

C
13 years

D
14 years

Solution

Let R's age be x years.
Then, Q's age = 2x years
P's age = (2x + 2) years

As per the given information in the question, we have
(2x + 2) + 2x + x = 27
5x = 25
x = 5

Hence, Q's age = 2x = 10 years
Question 5
1 / -0

A boat travels a certain distance at a speed of 11 km/hr upstream and at 5 km/hr downstream. Find the speed of boat in still water.

A
7 km/hr

B
8 km/hr

C
9 km/hr

D
10 km/hr

Solution

Let the speed of boat in still water be a.
And let the speed of river be b.
Upstream speed = a - b
Downstream speed = a + b

So, a - b = 5 (Upstream speed)
a + b = 11 (Downstream speed)

Adding these equations, we get
2a = 16
a = 8

Speed of boat in still water = 8 km/hr