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 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.

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