Olympiad Test: Linear Equations - Class 8 MCQ

If she has 7 pieces totally, it means that one of those pieces is the uncut half, and the other half is cut into 6 pieces. Each of those 6 pieces has a weight of 20 gm which totally weighs 6*20= 120gm. If one half is 120 gm, then so is the other. Therefore the total weight of the cake is 120*2= 240 gm.

Let's analyze the sequence and determine how many even numbers satisfy the conditions:

Sequence: 3, 8, 4, 1, 5, 7, 2, 8, 3, 4, 8, 9, 3, 9, 4, 2, 1, 5, 8, 2

Step-by-Step Analysis:

1. Number 8 (2nd position):

   • Preceding number: 3 → 8 is not divisible by 3.
   • Following number: 4 → Condition not met, ignore this 8.

2. Number 4 (3rd position):

   • Preceding number: 8 → 4 is not divisible by 8.
   • Following number: 1 → Condition not met, ignore this 4.

3. Number 2 (7th position):

   • Preceding number: 7 → 2 is not divisible by 7.
   • Following number: 8 → Condition not met, ignore this 2.

4. Number 8 (8th position):

   • Preceding number: 2 → 8 is divisible by 2.
   • Following number: 3 → 8 is not divisible by 3.
   • Condition met: Include this 8.

5. Number 4 (10th position):

   • Preceding number: 3 → 4 is not divisible by 3.
   • Following number: 8 → Condition not met, ignore this 4.

6. Number 8 (11th position):

   • Preceding number: 4 → 8 is divisible by 4.
   • Following number: 9 → 8 is not divisible by 9.
   • Condition met: Include this 8.

7. Number 4 (15th position):

   • Preceding number: 9 → 4 is not divisible by 9.
   • Following number: 2 → Condition not met, ignore this 4.

8. Number 2 (16th position):

   • Preceding number: 4 → 2 is not divisible by 4.
   • Following number: 1 → Condition not met, ignore this 2.

9. Number 8 (19th position):

   • Preceding number: 5 → 8 is not divisible by 5.
   • Following number: 2 → Condition not met, ignore this 8.

10. Number 2 (20th position):

    • This is the last number in the sequence, so no following number to check.

Conclusion:

The numbers that satisfy the conditions are the 8 at positions 8 and 11.

Thus, the correct answer is b) Two.

(b) contain two variable

Let S1 = x and S2 = x+10
Distance = speed * time
D1= 3x, D2 = 3(x+10)
Total distance = D1+D2+20
230 = 3x+30+3x+20
6x = 180
x = 30 km/h
x+10 = 40 km/h

• • Let’s assume the original number of men is M.
  • The provisions last for 21 days for M men.

• Calculate Total Provisions:

  • Total provisions can be represented as:
    • Total Provisions = Number of Men × Number of Days
    • So, Total Provisions = M × 21

• Determine the New Scenario:

  • Now, only one-seventh of the original number of men will be consuming the provisions.
    • New Number of Men = M/7

• Set Up the Equation for the New Scenario:

  • Let’s denote the number of days the provisions will last in the new scenario as D.
  • Using the proportionality:
    • New Number of Men × New Number of Days = Total Provisions
    • So, (M/7) × D = M × 21

• Simplify the Equation:

  • Divide both sides of the equation by M to eliminate M:
    • D/7 = 21

• Solve for D:

  • Multiply both sides by 7:
    • D = 21 × 7
    • D = 147

Let 1 person do 1 unit of work in 1 day
When 25 people are employed, amount of work in 1 day = 25 units
Amount of work in 16 days = 25*16 = 400
After 16 days, 5 more people are employed and work is completed in 15 days
So work done in next 15 days = 30*15 = 450
If those 5 people are not employed , No. of days needed to complete 450 units of work = 450/25 = 18
But they were supposed to complete the work by 16 days
Hence 2 extra days are needed by 25 people.

The problem involves a bullet train that:

• Leaves at x hours and y minutes
• Reaches its destination at y hours and z minutes on the same day
• The total travel time is z hours and x minutes

Step-by-Step Analysis

Since the train departs and arrives on the same day, we know that:

1. The travel time (z hours and x minutes) should fit within a 24-hour period.
2. The departure time (x hours and y minutes) also falls within the range of a 24-hour clock, meaning x represents an hour in the day.

Possible Values for x

Given that x represents an hour on a 24-hour clock, it can take any integer value from 0 to 23. This is because hours in a day range from 0 (midnight) to 23 (11 PM).

Therefore, there are 24 possible values for x, ranging from 0 to 23.

Conclusion

Since the question asks for the number of possible values of x, the answer is 24. None of the provided options (1, 2, 3, or 4) match this, so the correct answer is: None of these.

We have, 

⇒ 

553x − 41 = 38x+34 ⇒ 15x = 75

 ⇒ x = 75/15 = 5

Let the number be x. Then, One-third of x = x/3, Quarter of x = x/4
One-twelfth of x = x/12
Average of third, quarter and one-twelfth of 

According to question, we have 


⇒ 
⇒ 
⇒ 36x − 4x − 3x − x = 36 × 56 ⇒ 28x = 36 × 56
⇒ 

Hence, the number is 72. 

Let the number bex.
According to question, we have 
 

Hence, the number is 15.

We have,6(3x+2)−5(6x−1)

= 6(x−3)−5(7x−6)+12x

⇒18x+12−30x+5

= 6x−18−35x+30+12x

⇒ 5x=−5 ⇒ x=−1

Ratio of two parts = 5:8

Smaller number
Larger number  

So, the product of the number 

= 115 × 184 = 21160

Let the number be x. According to question, we have 

Let the length of rectangle be x cm. Width of rectangle  

∴ Area of rectangle = length × width 
Also, perimeter of rectangle = 2(length + width) Now, according to question. 

Let the number be x. According to question, we have 

Let units place digit be x. So tens place digit = 9 − x. 

∴ The original number = 10(9-x)+x = 90-10x + x=90 - 9x Now, after interchanging the digits, the number formed = 10 (x) + 9 - x = 9x + 9 

∴ According to question, we have 90 - 9x - 27 = 9x + 9 

⇒ −18x = −54 ⇒ x = 3

So, the original number 

= 90−9×3 = 63

Let numerator be x, then denominator is x+3. 

∴ The original rational number 
Now, according to question 

On cross multiplying, we get  5(x−3 )= x+5

 ⇒ 5x−15 = x+5 ⇒ 5x−x = 5+15

 ⇒ 4x = 20 ⇒ x = 20/4 = 5

Hence, the original rational number is