Equations in One Variable Test

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Equations in One Variable Test - 3

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Weekly Quiz Competition

Question 1
1 / -0

If 15 is subtracted from 15 times a number, then the result is 30 more than 12 times the number. What will be 3 more than three times this number?

A
48

B
12

C
18

D
45

Solution

Let the number be x.
According to the question:
15x – 15 = 30 + 12x
15x – 12x = 30 + 15
3x = 45
x = 45/3 = 15
∴ 3x + 3 = 3 × 15 + 3
= 45 + 3 = 48
Question 2
1 / -0

A car covers a distance from station A to B with a certain speed. If its speed is increased by 2 km/hr, then it will cover the same distance in 4 hours. It will cover the same distance in 5 hours if its speed is decreased by 2 km/hr. What is the original speed of the car?

A
16 km/hr

B
18 km/hr

C
20 km/hr

D
22 km/hr

Solution

Let the original speed be x km/hr.
According to the question,
(x + 2) × 4 = (x – 2) 5 (D = S × t)

4x + 8 = 5x – 10
x = 18 km/hr
Question 3
1 / -0

For a given triangle ABC, the length of BC is twice that of AB and length of AC is thrice that of AB. If 5 cm is added to the length of AB, 7 cm is added to length of BC and 6 cm is added to the length of AC, then sum of all the new sides will become 6 cm more than twice the sum of the original sides. What is the original length of BC?

A
6 cm

B
2 cm

C
4 cm

D
1 cm

Solution

For ΔABC,
AB = x cm
BC = 2x cm
AC = 3x cm

Then sum = AB + BC + CA
= x + 2x + 3x = 6x

Now, new sides will be
AB = (x + 5) cm
BC = (2x + 7) cm
AC = (3x + 6) cm

New sum = (x + 5) + (2x + 7) + (3x + 6)
= 6x + 18

According to the question,
6x + 18 = 2(6x) + 6
6x + 18 = 12x + 6

6x – 12x = 6 – 18
– 6x = – 12
6x = 12
x = 2

∴ Original length of BC = 2x cm = 2 × 2 cm = 4 cm
Question 4
1 / -0

In an examination, the ratio of Rahul's correct answers to his incorrect answers was 7 : 5. If the number of correct answers was 8 more than the incorrect answers, then how many questions in all did he attempt in the exam?

A
36

B
52

C
48

D
56

Solution

Let the number of Rahul's correct answers be 7x.
∴ Incorrect answers = 5x

According to the question,
7x = 5x + 8

Step 1
Subtract 5x from both sides.
7x – 5x = 5x + 8 – 5x
2x = 8

Step 2
Divide both sides by 2.
x = 8/2
x = 4

∴ Correct answers = 7x = 28
Incorrect answer = 5x = 20

∴ Total questions attempted by Rahul = 28 + 20 = 48
Question 5
1 / -0

The present age of Sham is 3 more than the present age of Ram. If after 5 years, twice the age of Ram and the age of Sham will add up to give 69, then what is the present age of Sham?

A
51 years

B
17 years

C
29 years

D
20 years

Solution

Let present age of Ram be x years.
∴ Present age of Sham will be x + 3 years.

After 5 years,
2(x + 5) + (x + 3 + 5) = 69
2x + 10 + x + 8 = 69
3x + 18 = 69
3(x + 6) = 69

Step 1
Dividing both sides by 3.
x + 6 = 69/3
x + 6 = 23

Step 2
Subtracting 6 from both sides.
x + 6 – 6 = 23 – 6
x = 17

∴ Age of Ram = 17 years
Age of Sham = (17 + 3) = 20 years
Question 6
1 / -0

If the sum of three consecutive integers is 72, then which of the following numbers is the greatest among them?

A
23

B
24

C
25

D
26

Solution

Let one number be x.
Then, other numbers will be x + 1 and x + 2.

According to the question,
x + x + 1 + x + 2 = 72
3x + 3 = 72
3(x + 1) = 72

x + 1 = 72/3 = 24
x = 24 – 1 = 23

∴ The numbers will be 23, 24, 25.

The greatest number obtained is 25.
Question 7
1 / -0

The sum of length and breadth of a rectangle is 12 cm. If five times the length and seven times the width makes a total of 70 cm, what is the area of the rectangle?

A
50 cm²

B
65 cm²

C
70 cm²

D
35 cm²

Solution

Let the length be x cm.
Then, breadth will be (12 – x) cm.

According to the question,
5x + 7(12 – x) = 70
5x + 84 – 7x = 70

– 2x + 84 = 70
– 2x = 70 – 84
– 2x = – 14
x = 7

∴ Length = 7 cm

Breadth = (12 – 7) = 5 cm
∴ Product = l × b = 7 × 5 = 35 cm²

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Re-Attempt Weekly Quiz Competition

Equations in One Variable Test - 3

Result

Equations in One Variable Test - 3

Score

-

Rank

-

SHARING IS CARING

Question 1

48

12

18

45

Solution

Question 2

16 km/hr

18 km/hr

20 km/hr

22 km/hr

Solution

Question 3

6 cm

2 cm

4 cm

1 cm

Solution

Question 4

36

52

48

56

Solution

Question 5

51 years

17 years

29 years

20 years

Solution

Question 6

23

24

25

26

Solution

Question 7

50 cm2

65 cm2

70 cm2

35 cm2

Solution

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50 cm²

65 cm²

70 cm²

35 cm²