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All questions of Quantitative Aptitude and Reasoning for Class 8 Exam

A playground which is 250 m long and 20 m broad is to be fenced with wire. How much wire is needed?
  • a)
    270 m
  • b)
    230 m
  • c)
    540 m
  • d)
    None of these
Correct answer is option 'C'. Can you explain this answer?

Clearly, the playground is of rectangular shape.
So the required length of the wire
= Perimeter of the rectangle
= 2 (length + breadth)
= 2 (250+20) = 540 m.

In an election between two candidates, one got 55% of the total valid votes, 20% of the votes were invalid. If the total number of votes was 7500, the number of valid votes that the other candidate got, was:
  • a)
    2500
  • b)
    2700
  • c)
    2900
  • d)
    3100
Correct answer is option 'B'. Can you explain this answer?

Aaditya Iyer answered
Given:
- Total number of votes = 7500
- 20% of the votes were invalid

To find:
- The number of valid votes that the other candidate got

Methodology:
1. Calculate the number of invalid votes.
2. Subtract the number of invalid votes from the total votes to find the number of valid votes.
3. Calculate the number of valid votes received by the other candidate using the given percentage.

Solution:

1. Calculate the number of invalid votes:
- 20% of the total votes = 20/100 * 7500 = 1500 votes

2. Calculate the number of valid votes:
- Total votes - Invalid votes = 7500 - 1500 = 6000 votes

3. Calculate the number of valid votes received by the other candidate:
- The other candidate received 55% of the total valid votes.
- So, the number of valid votes received by the other candidate = 55/100 * 6000 = 3300 votes

Therefore, the number of valid votes that the other candidate got is 3300 votes, which corresponds to option 'B'.

In a class of 60, where girls are twice that of boys, Kamal ranked seventeenth from the top. If there are 9 girls ahead of Kamal, how many boys are after him in rank ?
  • a)
    3    
  • b)
    7
  • c)
    12    
  • d)
    23
Correct answer is option 'C'. Can you explain this answer?

Given information:
- Total number of students in the class = 60
- Girls are twice the number of boys
- Kamal is ranked 17th from the top
- There are 9 girls ahead of Kamal

Finding the number of boys and girls in the class:
Let the number of boys be x. Since girls are twice the number of boys, the number of girls would be 2x.

Total number of students in the class = Number of boys + Number of girls
60 = x + 2x
60 = 3x
x = 20

Therefore, there are 20 boys and 40 girls in the class.

Finding the number of students ahead of Kamal:
Since Kamal is ranked 17th from the top and there are 9 girls ahead of him, the number of students (including Kamal) ahead of him would be 17 + 9 = 26.

Finding the number of boys after Kamal:
The number of boys after Kamal would be the total number of boys minus the number of boys ahead of Kamal.

Number of boys after Kamal = Number of boys - Number of boys ahead of Kamal
= 20 - 26
= -6

Since the number of boys after Kamal cannot be negative, it means that there are no boys after Kamal in rank. Therefore, the answer is option C) 12.

The ratio of the age of a father to that of his son is 5 : 2. If the product of their ages in years is 1000, then find the father’s age after 10 years.
  • a)
    40 years
  • b)
    50 years
  • c)
    60 years
  • d)
    100 years
Correct answer is option 'C'. Can you explain this answer?

Pratima jain answered
's age.

Let the age of the father be 5x and the age of the son be 2x (according to the given ratio).
Their product of ages is 1000, so we have:

5x * 2x = 1000
10x^2 = 1000
x^2 = 100
x = 10

Therefore, the age of the father is 5x = 50 years old.

If one angle of a triangle is equal to the sum of the other two angles, the triangle must be:
  • a)
    Scalene    
  • b)
    Right Angled
  • c)
    Obtuse Angled    
  • d)
    Acute Angled
Correct answer is option 'B'. Can you explain this answer?

Mansi mehta answered


Explanation:

Right Angled Triangle:
- In a right-angled triangle, one angle is a right angle, which is equal to 90 degrees.
- The other two angles are acute angles, which are less than 90 degrees.
- The sum of the two acute angles in a right-angled triangle is always equal to 90 degrees.

Given condition:
- One angle of the triangle is equal to the sum of the other two angles.
- Let the angles be x, y, and z, where x is the angle that is equal to the sum of y and z.
- Therefore, x = y + z.
- According to the given condition, x = y + z.

Conclusion:
- Since the given condition x = y + z is satisfied in a right-angled triangle, the triangle must be a right-angled triangle.
- Therefore, the correct answer is option 'B' - Right Angled Triangle.

Varun purchased a book and sold it at a profit of 20% to Vijay. If Vijay paid? ₹ 1440 to Varun, then at what price did Varun buy the book?
  • a)
    ₹ 1000
  • b)
    ₹ 1150
  • c)
    ₹ 1200
  • d)
    ₹ 1100
Correct answer is option 'C'. Can you explain this answer?

Rajat Singh answered
Understanding the Problem
Varun sold a book to Vijay for 1440 with a profit of 20%. We need to find out the price at which Varun originally bought the book.
Calculating the Cost Price
To find the cost price (CP), we can use the formula for selling price (SP) in relation to profit percentage:
- Selling Price = Cost Price + Profit
- Profit = Cost Price * Profit Percentage
Since the profit percentage is 20%, this can be expressed as:
- Profit = Cost Price * 20/100 = Cost Price * 0.2
Now, we can rewrite the Selling Price equation:
- Selling Price = Cost Price + (Cost Price * 0.2)
This simplifies to:
- Selling Price = Cost Price * (1 + 0.2) = Cost Price * 1.2
Setting Up the Equation
Given that the Selling Price is 1440, we have:
- 1440 = Cost Price * 1.2
Solving for Cost Price
To find the Cost Price, we rearrange the equation:
- Cost Price = 1440 / 1.2
Calculating:
- Cost Price = 1440 / 1.2 = 1200
Conclusion
Thus, the price at which Varun bought the book is:
- 1200
Therefore, the correct answer is option 'C'.

If in a certain code, HAT is 782, RABBIT is 681192. Then how will HABIT be coded as ?
  • a)
    78139
  • b)
    78192
  • c)
    68192
  • d)
    78129
Correct answer is option 'B'. Can you explain this answer?

To determine the code for the word HABIT, we need to analyze the given codes for the words HAT and RABBIT.

Given:
HAT is coded as 782
RABBIT is coded as 681192

Let's break down the codes and observe the pattern:

1. Code for HAT (782):
- The word HAT has three letters.
- The code consists of three digits.
- The first digit (7) represents the first letter 'H'.
- The second digit (8) represents the second letter 'A'.
- The third digit (2) represents the third letter 'T'.

2. Code for RABBIT (681192):
- The word RABBIT has six letters.
- The code consists of six digits.
- The first digit (6) represents the first letter 'R'.
- The second digit (8) represents the second letter 'A'.
- The third digit (1) represents the third letter 'B'.
- The fourth digit (1) represents the fourth letter 'B'.
- The fifth digit (9) represents the fifth letter 'I'.
- The sixth digit (2) represents the sixth letter 'T'.

From the given examples, we can observe that the code for each letter is determined by its position in the word. Therefore, the code for the word HABIT can be determined as follows:

- The word HABIT has five letters.
- The code should consist of five digits.
- The first digit should represent the first letter 'H'.
- The second digit should represent the second letter 'A'.
- The third digit should represent the third letter 'B'.
- The fourth digit should represent the fourth letter 'I'.
- The fifth digit should represent the fifth letter 'T'.

Based on this pattern, we can conclude that the code for HABIT is 78192. Therefore, the correct answer is option B: 78192.

An insect crawls up 5 cm every second on a 60 cm vertical rod and then falls down 2 cm over the next second. How many seconds will it take to climb the rod?
  • a)
    10
  • b)
    20
  • c)
    30
  • d)
    39
Correct answer is option 'D'. Can you explain this answer?

Calculation:
- The insect climbs 5 cm every second and falls 2 cm every second.
- So, in every 2 seconds, it climbs 5 cm - 2 cm = 3 cm.
- To climb a 60 cm rod, it will take 60 cm / 3 cm per 2 seconds = 20 cycles of 2 seconds each.
- Therefore, it will take 20 cycles x 2 seconds = 40 seconds to climb the rod.

Correct Answer: Option D) 39

In a box, (3/4)th of the balls are red, (1/6)th are white and the rest are blue. If there are 3 blue balls in the box, how many are red?
  • a)
    9
  • b)
    18
  • c)
    27
  • d)
    39
Correct answer is option 'C'. Can you explain this answer?

Given:
- (3/4)th of the balls are red
- (1/6)th are white
- Rest are blue
- 3 blue balls in the box

To find:
- Number of red balls

Solution:
Let the total number of balls in the box be 'x'.

- (3/4)x = number of red balls
- (1/6)x = number of white balls
- 3 = number of blue balls

We can find the total number of balls as follows:

x = (3/4)x + (1/6)x + 3
x - (3/4)x - (1/6)x = 3
(7/12)x = 3
x = (3*12)/7 = 36/7 (approx. 5.14)

Since the number of balls can only be a whole number, we can assume that there are 5 balls in the box.

- (3/4)*5 = 15/4 (approx. 3.75)
- (1/6)*5 = 5/6 (approx. 0.83)
- 5 - 3 = 2

Thus, there are 15/4 (approx. 3.75) red balls in the box.

Answer: Option C (27)

What is the value of 0 - 1 + 2 - 3 + 4 - 5 + 6 - 7 ........... - 17 + 18 - 19 + 20?
  • a)
    10
  • b)
    15
  • c)
    20
  • d)
    25
Correct answer is option 'A'. Can you explain this answer?

Kiran Reddy answered
0 - 1 + 2 - 3 + 4 - 5 + 6 - 7...... - 17 + 18 - 19 + 20
= 0 + (-1 + 2) + (-3 + 4) + (-5 + 6) + ...... + (-17 + 18) + (-19 + 20)  
= 0 + 1 + 1 + ...... + 1 + 1 = 10

If' +' means' divided by '-',means ' added to', 'x' means 'subtracted from' and '÷' means 'multiplied by1, then what is the value of 24 ÷ 12 - 18 + 9 ?
  • a)
    - 25
  • b)
    0.72
  • c)
    15.30
  • d)
    290
Correct answer is option 'D'. Can you explain this answer?

Megha bhatia answered
Understanding the Problem
To solve the expression "24 ÷ 12 - 18 + 9" using the unique definitions provided for the operators, we need to replace each symbol with its corresponding mathematical operation.
Symbol Replacement
- "+" means "divided by" (÷)
- "-" means "added to" (+)
- "x" means "subtracted from" (-)
- "÷" means "multiplied by 1" (×)
Let's rewrite the expression based on these definitions:
Expression Transcription
- Original: 24 ÷ 12 - 18 + 9
- Replacing symbols:
- 24 (multiplied by 1) 12 (added to) 18 (divided by) 9
This translates to:
24 × 12 + 18 ÷ 9
Calculating the Expression
1. Calculate 24 × 12:
24 × 12 = 288
2. Calculate 18 ÷ 9:
18 ÷ 9 = 2
3. Now add the results:
288 + 2 = 290
Final Result
Thus, the value of the expression "24 ÷ 12 - 18 + 9" after converting the symbols and performing the calculations is:
290
Therefore, the correct answer is option 'D'.

What number should replace the question mark ?
  • a)
    2
  • b)
    9
  • c)
    12
  • d)
    19
Correct answer is option 'A'. Can you explain this answer?

Kiran Reddy answered
Subtract the sum of the even numbers from the sum of the odd numbers.
7+9 = 16    9+3 = 12
2+4 = 6    4+6 = 10
16-6=10    12-10 = 2

Select from the alternative, the box that can be formed by folding the sheet shown in figure (X).

  • a)
    A only
  • b)
    A, B, and C only
  • c)
    B and C only
  • d)
    A, B, C and D
Correct answer is option 'D'. Can you explain this answer?

Kiran Reddy answered
When the sheet in fig.(X) is folded to form a cube, then the face bearing a dot appears opposite to a blank face, the face bearing a “+’ sign appears opposite to another blank face and the face bearing a circle appears opposite to the third blank face. Clearly, all the four cubes shown in figures (A), (B), (C) and (D) can be formed.

Direction: In the following examples there is a diagram marked (X), with one or more dots placed in it. The diagram is followed by four other figures, marked (a), (b), (c) and (d) only one of which is such as to make possible the placement of the alternative in each of these
  • a)
  • b)
  • c)
  • d)
Correct answer is option 'B'. Can you explain this answer?

Kiran Reddy answered
In figure (X), one of file dots lies in the region common to the circle and the triangle only and the other dot lies in the region common to die circle and die square only. In figures (a), (c) and (d), the region common to the circle and the triangle lies within the square. Only figure (b) contains a region common to the circle and the triangle only and also a region common to the circle and the square.

  • a)
    11
  • b)
    12
  • c)
    22
  • d)
    33
Correct answer is option 'C'. Can you explain this answer?

Kiran Reddy answered
Moving clockwise,
We have: 594÷3 = 198:198÷3 = 66. So, missing number = 66 ÷ 3 = 22

Which of the following diagrams correctly represents the relationship among smokers, bidi smokers, cancer patients?
  • a)
  • b)
  • c)
  • d)
Correct answer is option 'B'. Can you explain this answer?

Kiran Reddy answered
Bidi smokers is a subset of smokers cancer patient may be a smoker, bidi smoker and non smoker. Hence, third object shares a common relationship with first and second object as well.

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