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General Test - 5

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Weekly Quiz Competition
  • Question 1
    4 / -1

    Three men and \(4\) women can do a piece of work in \(7\) days, whereas \(2\) men and \(1\) woman can do it in \(14\) days. Seven women will complete the same work in:

    Solution

    Given:

    \(3\) men and \(4\) women can do a piece of work in \(7\) days and, \(2\) men and \(1\) woman can do it in \(14\) days

    As we know,

    \(M_{1} D_{1}=M_{2} D_{2}\), where \(M_{1}\) and \(M_{2}=\) Number of person, \(D_{1}\) and \(D_{2}=\) Number of days

    Total Work \(=\) Efficiency \(\times\) Time

    \(M_{1}D_{1}=M_{2} D \)

    \(\Rightarrow(3 \) men \(+4 \) women \() \times 7=(2\) men \(+1\) women \() \times 14 \)

    \(\Rightarrow(3\)men \(+4\) women \()=(2 \) men \(+1\) women \() \times 2 \)

    \(\Rightarrow 3 \) men \(+4 \) women \(=4 \) men \(+2\) women

    \(\Rightarrow 2\) women \(=\) men 

    \(\Rightarrow\) (women : men) \(=1: 2\)

    \(\Rightarrow\) Efficiency Ratio of (women : men) \(=1: 2\)

    \(\Rightarrow\) Total Work \(=\) Efficiency \(\times\) Time

    \(\Rightarrow(3\) men \(+4\) women \() \times 7=(2\) men \(+1\) women \() \times 14\)

    \(\Rightarrow(3 \times 2+4 \times 1) \times 7=(2 \times 2+1 \times 1) \times 14\)

    \(=70\)

    \(\Rightarrow\) Total Work \(=70\)

    \(\Rightarrow\) number of days to complete the work by \(7\) women \(=\frac{\text{ Total work}}{\text{Efficiency}}\)

    \(= \frac{70 }{(7 \times 1)}\)

    \(= 10\) days

    \(\therefore\) Required number of days to complete the work by \(7\) women is \(10\) days.

  • Question 2
    4 / -1

    A alone can complete the work in 12 days and B alone can complete the work in 24 days. When A, B and C worked together then work will be completed in \(\frac{72}{11}\) days. In how many days C alone can complete the half of the work?

    Solution

    Given:

    A can do the work in 12 days.

    B can do the work in 24 days.

    A, B, C can do the work in \(\frac{72}{11}\) days.

    A's 1 days work \(= \frac{1}{12}\)

    B's 1 days work \(= \frac{1}{24}\)

    ⇒ (A + B + C)'s 1 days work \(= \frac{1}{12} + \frac{1}{24} + \frac{1}{C}\)

    \(⇒ \frac{1}{12} + \frac{1}{24}+ \frac{1}{C} = \frac{11}{72}\)

    \(⇒ \frac{1}{C} =\frac{ 1}{36}\)

    C alone can complete the work in 36 days.

    ∴ Time taken by C to complete half of work \(= 36 × \frac{1}{2} = 18\) days

  • Question 3
    4 / -1

    If the sum of the dimensions of a rectangular parallelepiped is \(24\) cm and the length of the diagonal is \(15\) cm, then the total surface area of it is:

    Solution

    Let, length \(=a\) cm, breadth \(= b\) cm , height \(= c\) cm

    \(\therefore a+b+c=24\)...... (i)

    and \(\sqrt{a^2+b^2+c^2}=15\)

    \(\Rightarrow a^2+b^2+c^2=15 \times 15=225\) ....... (ii) 

    \(\therefore(a+b+c)^2=a^2+b^2+c^2+2(a b+b c+c a)\)

    \(\Rightarrow 576=225+2(a b+b c+c a)\)

    =351 sq.cm

  • Question 4
    4 / -1

    The perimeter of an equilateral triangle is \(36 \sqrt{3} \mathrm{~cm}\). Find its height.

    Solution

    Perimeter of an equilateral triangle \(=3 \times\) side

    Height of an equilateral triangle \(=(\frac{\sqrt{3} }{ 2}) \times\) side

    \(3 \times \) side \(=36 \sqrt{3} \Rightarrow \) side \(=\frac{36 \sqrt{3} }{ 3}\) \(=12 \sqrt{3}\)

    Height of the triangle \(=(\frac{\sqrt{3} }{ 2}) \times 12 \sqrt{3}= 18\)

  • Question 5
    4 / -1

    Choose the box that is similar to the box formed from the given sheet of paper (X).

    Solution

    When the sheet in fig. (X) is folded to form a cube, then the face bearing a square lies opposite to the face bearing a circle. Therefore, the cubes are shown in figures (A) and (B) which have the faces bearing the square and the circle adjacent to each other, cannot be formed. Hence, only the cubes in figures (C) and (D) can be formed.

  • Question 6
    4 / -1

    Direction: Study the following information carefully and answer the question given below

    There are eight person A, B, C, D, E, F, G and H sitting around a circular table facing towards centre(not necessarily in the same order). C is sitting second to the right of G. E is sitting to the immediate left of A who is facing C. D is sitting between A and G, B is sitting fourth to the left of G who is sitting to the immediate left of H.

    Who is sitting at the immediate left of B?

    Solution

    1. C is sitting second to the right of G.

    2. A is facing C.

    3. E is sitting to the immediate left of A.

    4. D is sitting between A and G.

    5. G is to the immediate left of H.

    6. B is sitting fourth to the left of G.

  • Question 7
    4 / -1

    Four boys and four girls are sitting in the first row of a classroom, such that two girls are sitting at the second and the fifth position from the extreme left end, while one boy each is sitting to their immediate left. If no two boys are sitting together, then how many girls are sitting between the first and the fourth positions from the left end?

    Solution

    1) Two girls are sitting at the second and the fifth position from the extreme left end

    2) One boy each is sitting to their immediate left

    3) No two boys are sitting together

    This means that the other two boys are sitting at the sixth position from extreme left end and at the extreme right end

    Thus, the final arrangement is:

  • Question 8
    4 / -1

    Five children are sitting in a row. A is sitting next to B, but not C. D is sitting next to E, who is sitting on the extreme left and C is not sitting next to D. Who are sitting adjacent to A.

    Solution

    Children: A, B, C, D and E

    From the given information,

    1. Starting from: D is sitting next to E, who is sitting on the extreme left and C is not sitting next to D.

    Two cases are possible:

  • Question 9
    4 / -1

    Seven friends - Ajith, Bala, Hari, David, Raja, Sekar, and Guna - are sitting around a circular table. David is not the neighbor of Hari and Raja. Ajith is the neighbor of Bala and Hari. Guna, who is second to the left of David, is the neighbor of Sekar and Raja.

    What is the position of Hari?

    Solution

    Let us consider all of them facing inside.

    1) Guna, who is second to the left of David, is the neighbour of Sekar and Raja.

    2) David is not the neighbour of Hari and Raja. (So raja is immediate left of Guna)

    3) Ajith is the neighbour of Bala and Hari. (So, Hari is immediate right of Ajith)

    So, ‘Third to the left of Sekar’ is the correct answer.

  • Question 10
    4 / -1

    Direction: Study the information given below carefully and answer the question that follow.

    Six persons sit around the circular table facing towards the center. P sits immediate right of S. U sits second to the left of R. P and U are not adjacent to each other. Q and T are adjacent to U. Who sits second to the left of U?

    Solution

    Six Persons: P, Q, R, S, T and U

    1. P sits immediate right of S.

    2. P and U are not adjacent to each other.

    3. U sits second to the left of R.

    4. Q and T are adjacent to U.

    Therefore, P sits second to the left of U.

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