Please wait...

SSC GD 2025 Aptitude Test - 3
Result
SSC GD 2025 Aptitude Test - 3
  • /

    Score
  • -

    Rank
Time Taken: -
  • Question 1/10
    2 / -0.5

    What is the average of the prime numbers between 20 and 50?

    Solutions

    Formula:

    Average = Sum / Total number

    Calculation:

    The prime numbers between 20 and 50 is 23, 29, 31, 37, 41, 43, 47

    Total number of prime numbers = 7

    Sum of the prime numbers between 20 and 50 

    ⇒ 23 + 29 + 31 + 37 + 41 + 43 + 47

    ⇒ 251

    So, average of the numbers = 251 / 7 = 35.857

    ∴ The average is 35.857.

  • Question 2/10
    2 / -0.5

    The average age of a man and his son is 55 years. The ratio of their ages is 7 ∶ 4,respectively. What will be the ratio of their ages after 6 years?

    Solutions

    Given:

    The average age of a man and his son is 55 years.

    The ratio of their ages is 7 ∶ 4 and respectively. 

    Calculation:

    Let the age of the man and his son be 7x and 4x respectively.

    ​According to the question,

    (7x + 4x) = 55 × 2

    ⇒ 11x = 110

    ⇒ x = 10

    Now, the ratio of their ages after 6 years

    ⇒ (7 × 10 + 6) : (4 × 10 + 6)

    ⇒ 76 : 46 = 38 : 23

    ∴ The ratio of their ages after 6 years is 38 : 23.

  • Question 3/10
    2 / -0.5

    Aman had Rs.10,000 with him. He lent a part of it at 8% per annum simple interest and the remaining at 10% per annum. His total annual income was Rs. 880 Find the sum lent at 8%

    Solutions

    Given:

    Principal (P) = 10,000,

    Rate of interest(R) = 8% & 10%,

    Time (T) = 1 year

    Annual Income = Rs 880

    Formula used:

    S.I. = (P × R ×  T)/100

    Calculation:

    SI on the sum of 10,000 at the rate of 8% per annum = 10000 × 8/100

    = Rs 800

    Total annual Income = Rs 880

    Extra interest in 1 year = 880 - 800 = Rs 80

    (10 - 8) = 2% corresponds to Rs 80

    100% corresponds to Rs 4000

    Money invested on 2nd part = 4000

    Money invested on 1st part = 10000 - 4000 = 6000

    ∴ The sum lent on 8% is 6000.

  • Question 4/10
    2 / -0.5

    If the simple interest on a certain sum of money for 15 months at 9.6% per annum exceeds the simple interest on the same sum for 8 months at 11.4% by Rs. 1,320, then the sum is:

    Solutions

    Given:

    The simple interest on a certain sum of money for 15 months at 9.6% per annum exceeds the simple interest on the same sum for 8 months at 11.4% by Rs. 1,320

    Concept used:

    S.I = (P × T × R)/100

    Here, P = Sum, T = Time & R = Rate 

    Calculation:

    Let the sum be P

    Now, [P × 15/12 × 9.6/100] - [P × 8/12 × 11.4/100] = 1320

    ⇒ 0.12P - 0.076P = 1320

    ⇒ 0.044P = 1320

    ⇒ P = 1320/0.044

    ⇒ P = 30000

    ∴ The sum is Rs. 30,000.

    Alternate Method

    Calculation:

    According to the question,

    Principal is constant. So

    ⇒ (15/12) × 9.6% - (8/12) × 11.4% = 1320

    ⇒ (12 - 7.6)% = 1320

    ⇒ 4.4% = 1320

    ⇒ 100 % = (1320/4.4) × 100 = Rs. 30,000

    ∴ The correct answer is 30,000.

  • Question 5/10
    2 / -0.5

    If the radius of a right circular cylinder is decreased by 50% and its height is increased by 60%, its volume will be decreased by:

    Solutions

    Given:

    Radius decreased by 50%

    Height increased by 60%

    Shortcut Trick

    Convert percentage into fraction

    Alternate Method

    Concept used:

    Volume of the right circular cylinder (V) = πr2h

    Where, r = radius and h = height

    Percentage change:

    [(original value - new value) / original value] × 100

    Calculation:

    Let initial radius = r cm, Initial height = h cm

    So, Initial volume = πr2h

    Decreased radius = (r - 0.5r) = 0.5r cm

    Increased height = (h + 0.6h) = 1.6h cm

    So, new volume (V') = π × (0.5r)2 × (1.6h)

    ⇒ V' = 0.4πr2h

    Change in volume = (πr2h - 0.4πr2h) = 0.6πr2h

    Percentage change = [(0.6πr2h)/πr2h] × 100 = 60%

    ∴ The volume will be decreased by 60%

  • Question 6/10
    2 / -0.5

    Inside a circle with centre O, two equal chords of length 8 cm are drawn parallel to each other. If the distance between the chords is 6 cm, then find the area of the rhombus which can be formed between the chords whose two vertices lie on the circle and the other two lie on the chords.

    Solutions

    Given:

    Length of chords = 8 cm

    Distance between chords = 6 cm

    Concept:

    Since the chords are of equal length, they should lie on either side of the center and the distance of the chords from the center will be same.

    Perpendicular drawn from the centre to the chord of a circle bisects the chord.

    Firstly, calculate the value of the radius of the circle, the diameter of the circle will be one of the diagonals of the rhombus and the distance between the chords will be the other diagonal.

    Formula used:

    In right-angled triangle;

    H2 = P2 + B2

    Where,

    H → Hypotenuse

    P → Perpendicular

    B → Base

    Area of rhombus = 1/2 × d1 × d2

    Calculation:

    In ∆OBE;

    OE2 = OB2 + BE2

    ⇒ OE2 = 32 + 42

    ⇒ OE2 = 9 + 16

    ⇒ OE2 = 25

    ⇒ OE = √25 = 5 cm

    So, diameter AC = 5 + 5 = 10 cm

    Area of Rhombus ABCD = 1/2 × d1 × d2

    ⇒ 1/2 × AC × BD

    ⇒ 1/2 × 10 × 6

    ⇒ 30 cm2

    ∴ Area of Rhombus ABCD is 30 cm2

  • Question 7/10
    2 / -0.5

    Find total numbers that are divisible by 5 and 3 up to 950.

    Solutions

    Given:

    To find total numbers that are divisible by 5 and 3 up to 950

    Concept used:

    Last term in arithmetic progression or an = [a + (n - 1)d]

    Where, d = difference between consecutive terms, n = number of terms, a = first term, an = last term

    Calculation:

    Last term divisible by 15 ( both 3 and 5) up to 950 (an)= 945

    The first term divisible by 15 is 15 itself, a = 1, and d = 15 

    an = [a + (n - 1)d]

    ⇒ 945 = 15 + (n -1) x 15 

    ⇒ 930 = (n -1) x 15

    ⇒ 62 = n - 1

    ⇒ n = 62 + 1 = 63

    ∴ The answer is 63 .

  • Question 8/10
    2 / -0.5

    Which of the following is a rational number?

    Solutions

    Concept Used:

    1. Real numbers-

    Real numbers can be divided into rational numbers and irrational numbers.

    2. Rational numbers-

    rational number is a type of real number that is in the form of p/q where q is not equal to zero.

    3. Irrational numbers-

    Irrational numbers are real numbers that cannot be represented as simple fractions.

    An irrational number cannot be expressed as a ratio, such as p/q, where p and q are integers, q≠0.

    Explanation:

    Real numbers are divided into two categories, rational numbers and irrational numbers.

    Numbers in Option 02 and 04 are imaginary numbers, thus we can't categorize them into rational or irrational numbers.

    ∴ The rational number is 2, which is Option 03.

  • Question 9/10
    2 / -0.5

    When the price of a watch was reduced by 20%, the number of watches sold is increased by 40%. What was the effect on the sales in percentage?

    Solutions

    Given:

    The price of a watch is reduced to 20%

    The number of watches sold has increased by 40%

    Formula used:

    effective percentage change =  x + y + (xy/100)

    Calculation:

    Since first it is reduced to 20% and then it has increased by 40%

    Effective percentage  change = - x + y - (xy/100)

    ⇒ -20 +40 - 800/100 =  +12

    Here + sign shows an increase in the percentage

    ∴ The effect on sales in percentage is a 12% increase.

  • Question 10/10
    2 / -0.5

    2 candidates contested an election. The winning candidate got 52% of the valid votes and won by a margin of 360 votes. If 10% of votes were declared invalid, then what was the total number of votes polled?

    Solutions

    Given:

    Winning candidate received 52% of the valid votes.

    The winning candidate won by a margin of 360 votes.

    10% of the votes were declared invalid.

    Formula:

    Let the total number of votes polled be denoted as "T".

    Let the percentage of valid votes be denoted as "p" (which is 100% - 10% = 90%)

    Let the number of valid votes be denoted as "V" (which is 90% of T).

    Let the number of votes received by the winning candidate be denoted as "W" (which is 52% of V).

    Let the number of votes received by the losing candidate be denoted as "L" (which is 48% of V).

    Since the winning candidate won by a margin of 360 votes, we have:

    W - L = 360

    Solution:

    Since the winning candidate received 52% of the valid votes, we have:

    W = 52% of V

    or

    W = (52/100) × V

    Similarly, the losing candidate received 48% of the valid votes, we have:

    L = 48% of V

    or

    L = (48/100) × V

    Substituting the values of W and L in the equation W - L = 360, we get:

    (52/100) × V - (48/100) × V = 360

    Simplifying the above equation, we get:

    (4/100) × V = 360

    or

    V = (360 × 100)/4

    or

    V = 9000

    Therefore, the total number of votes polled is:

    T = V / 0.9 (since valid votes are 90% of total votes)

    or

    T = 9000 / 0.9

    or

    T = 10000

    Hence, the total number of votes polled is 10000.

User Profile
-

Correct (-)

Wrong (-)

Skipped (-)


  • 1
  • 2
  • 3
  • 4
  • 5
  • 6
  • 7
  • 8
  • 9
  • 10
Get latest Exam Updates
& Study Material Alerts!
No, Thanks
Click on Allow to receive notifications
×
Open Now