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SSC CHSL 2024 Aptitude Test - 3
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SSC CHSL 2024 Aptitude Test - 3
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  • Question 1/10
    2 / -0.5

    In a mixture of 624 litres, the ratio of milk and water is 5 ∶ 3. The amount of water to be further added to the mixture so as to make the ratio of the milk to water 5 ∶ 4 will be:

    Solutions

    Given data:

    Initial  624 litres

    Initial ratio of milk to water: 5 ∶ 3

    Desired ratio of milk to water: 5 ∶ 4

    Concept:

    To keep the amount of milk constant, calculate the amount of water that needs to be added to achieve the desired ratio.

    Calculation:

    ⇒ Volume of milk = 5 / (5 + 3) x 624 litres = 390 litres

    ⇒ Volume of water in new mixture = 4 / 5 x 390 litres = 312 litres

    ⇒ Volume of water to be added = (3 / (5 + 3) x 624 litres)  - 312 = 78 litres

    Therefore, 78 litres of water needs to be added to achieve the desired ratio.

  • Question 2/10
    2 / -0.5

    Find the value of n, when 2-7 × 23n+4 = 211 ÷ 2.

    Solutions

    Given:

    2-7 × 23n+4 = 211 ÷ 25

    Concept Used:

    With the same base in multiplication, the power gets added while in the division, the power gets subtracted.

    Calculation:

    ⇒ 2-7 × 23n+4 = 211 ÷ 25

    ⇒ 2-7+3n+4 = 211–5

    ⇒ 23n–3 = 26

    Equating the powers, we get

    ⇒ 3n – 3 = 6

    ⇒ 3n = 6 + 3 = 9

    ⇒ n = 9/3 = 3

    Therefore, the required value of n is 3.

  • Question 3/10
    2 / -0.5

    A, B and C can complete a work in 10, 15 and 30 days respectively. A and B started the work but B left after 3 days and C joined A. In how many days was the work completed?

    Solutions

    Given:

    A can complete the work in 10 days 

    B can complete the work in 15 days 

    C can complete the work in 30 days

    A and B started to work and after 3 days B left and C joined A on the work.

    Formula used:

    The efficiency of a person is the inverse of the time taken

    Calculation:

    Per day efficiency of A and B together = 1/10 + 1/15 = 1/6

    Per day efficiency of A and C together = 1/10 + 1/30 = 2/15

    Total work done by A and B in 3 days = 3 × (1/6) = 1/2

    Total work remaining = 1 - 1/2 = 1/2

    Let the A and C take n days to complete the remaining work

    ⇒ n × (2/15) = 1/2

    ⇒ n = 3.75

    ∴ Total time taken = 3 + 3.75 = 6.75 days

  • Question 4/10
    2 / -0.5

    Solutions

  • Question 5/10
    2 / -0.5

    In the table given below, there are two columns X and Y. Match the type of angle given in column X with the measures of the angle given in column Y:

    Solutions

    Calculation:

    Acute angle is < 90° so row A matches with d

    Obtuse angle is > 90° but less than 180° so, row B matches with c

    Straight line = 180° so, row C matches with a

    Right angle = 90 ° so, row D matches with b

    ∴ The correct answer is option 4

  • Question 6/10
    2 / -0.5

    The ratio of number of men and women in a ice-cream factory of 840 workers is 5 : 7. How many more men should be joined to make the ratio 1 : 1?

    Solutions

    Shortcut Trick

    Men : Women = 5 : 7

    Total number of workers = 840

    ⇒ The value of 12 → 840

    ⇒ The value of 1 → 70

    Since more men are joining. But the women are the same.

    ⇒ The value of 2 → 70 × 2 = 140

    Hence, 140 more men should be joined to make the ratio 1 : 1.

    Alternate Method

    Let the men and women in the ice-cream factory be 5x and 7x respectively.

    ⇒ 5x + 7x = 840

    ⇒ 12x = 840

    ⇒ x = 70

    Thus, Men = 5x = 5 × 70 = 350

    And women = 7x = 7 × 70 = 490

    Let y more men should be joined to make the ratio 1 : 1.

    ⇒ 350 + y = 490

    ⇒ y = 140

    Hence, 140 more men should be joined to make the ratio 1 : 1.

  • Question 7/10
    2 / -0.5

    On a sum of money, when invested for 2 years, compound interest and simple interest are ₹300 and ₹250, respectively. For both simple and compound interests the rate of interest per annum is the same, and for compound interest, interest is compounded annually. Find the rate of interest per annum.

    Solutions

    GIVEN:

    C.I. for 2 years = Rs300

    S.I. for 2 years = Rs250.

    Where C.I. = Compound Interest  , S.I. = Simple interest

    Concept Used:

    CALCULATION:

    S.I. for 2 years = Rs250 

    Hence, S.I. for 1 year = 250/2 = Rs125.

    Now, C.I. for 2 years = Rs300.

    Difference between C.I. and S.I. for 2 years = ( 300 -250) = Rs50.

    Hence, Required Rate of  Interest =( 50/ 125 ) × 100 = 40%.

    ∴ The required rate of interest is 40%.

  • Question 8/10
    2 / -0.5

    If the heights of two cylinders are in the ratio of 2 ∶ 3 and their-radius are in the ratio of 6 ∶ 5, then what is the ratio of the volumes of the cylinders?

    Solutions

    Given:

    The radii of two cylinders are in ratio 6 : 5

    The heights are in ratio 2 : 3

    Concept used:

    Volume of a cylinder = πr2h

    r = radius

    h = height

    Calculation:

    Let the radii of the two cylinders be 6x and 5x

    And height be 2y and 3y

    Now,

    Ratio = π(6x)22y : π(5x)23y

    ⇒ 72x2y : 75x2y

    ⇒ 24 : 25

    ∴ The ratio of their volumes is 24 : 25

  • Question 9/10
    2 / -0.5

    Two circles touch each other externally. The radius of the first circle with centre A is 18 cm. The radius of the second circle with centre B is 8 cm. Find the length of their common tangent CD.

    Solutions

    Given:

    Two circles touch each other externally

    Radius of first circle with centre A = 18 cm

    Radius of second circle with centre B = 8 cm

    Formula used:

    Where, d = r1 + r2 , r= radius of first circle ,r2 = radius of second circle 

    Calculation:

    Here, r1 = 18 cm , r2 = 8 cm 

    d = r1 + r2 = 18 + 8  = 26 cm 

    Now, as we know that

    Hence, the length of the direct common tangent CD is 24 cm .

  • Question 10/10
    2 / -0.5

    Directions For Questions

    The table given below shows the production of five companies in two years.

    ...view full instructions


    Which of the following statement is NOT correct?

    I. The average production of P, Q, R and S in year L are 172.5.

    II. The ratio of production of T in year L to the production of T in year M are 6 ∶ 7.

    Solutions

    Formula used:

    Average of N number = sum of N number/N 

    Calculation:

    Case I:

    Total production of P, Q, R, and S in the year L = 150 + 190 + 130 + 180 = 650

    Average production of P, Q, R, and S in the year L = 650/4 = 162.5

    Case I is incorrect.

    Case II:

    Production of T in the year of L = 120

    Production of T in the year of M = 140

    Required ratio = 120 : 140 = 6 : 7

    Case II is correct.

    ∴ The correct option is 2.

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