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Aptitude miscellaneous
  1. If the radius of a circle is decreased by 10%, then the area of the circle is decreased by








  1. View Hint View Answer Discuss in Forum

    Using Rule 12,

    Percentage decrease = 2x +
    x²
    		 %
    100

    = 2 × ( - 10) +
    (-10)²
    		 %
    100

    = (– 20 + 1)% = – 19%

    Correct Option: C

    Using Rule 12,

    Percentage decrease = 2x +
    x²
    		 %
    100

    = 2 × ( - 10) +
    (-10)²
    		 %
    100

    = (– 20 + 1)% = – 19%

  1. The outer circumference of a circular race-track is 528 metre. The track is everywhere 14 metre wide. Cost of levelling the track at the rate of Rs. 10 per sq. metre is :








  1. View Hint View Answer Discuss in Forum

    External radius of circular path = R metre
    ∴ 2πR = 528

    ⇒ 2 ×
    22
    		 × R = 528
    7

    ⇒ R =
    528 × 7
    		 = 84 metre
    2 × 22

    ∴ In-radius (r) = 84 – 14 = 70 metre
    ∴ Area of path = π(R² – r²)
    =
    22
    		(84² - 70²)
    7

    =
    22
    		(84 + 70)(84 - 70)
    7

    =
    22
    		 × 154 × 14 = 6776 sq. metre
    7

    ∴ Required cost = 6776 × 10 = Rs. 67760

    Correct Option: D

    External radius of circular path = R metre
    ∴ 2πR = 528

    ⇒ 2 ×
    22
    		 × R = 528
    7

    ⇒ R =
    528 × 7
    		 = 84 metre
    2 × 22

    ∴ In-radius (r) = 84 – 14 = 70 metre
    ∴ Area of path = π(R² – r²)
    =
    22
    		(84² - 70²)
    7

    =
    22
    		(84 + 70)(84 - 70)
    7

    =
    22
    		 × 154 × 14 = 6776 sq. metre
    7

    ∴ Required cost = 6776 × 10 = Rs. 67760

  1. If the area of a square is increased by 44%, retaining its shape as a square, each of its sides increases by :








  1. View Hint View Answer Discuss in Forum

    Increase in each side = x% (let)

    ∴ 2x +
    x²
    		 = 44
    100

    If x = 20
    ∴2x +
    x²
    		 = 2 × 20 +
    400
    		 = 44%
    100100

    Correct Option: D

    Increase in each side = x% (let)

    ∴ 2x +
    x²
    		 = 44
    100

    If x = 20
    ∴2x +
    x²
    		 = 2 × 20 +
    400
    		 = 44%
    100100

  1. What will be the percentage increase in the area of a square when each of the its sides is increased by 10%?








  1. View Hint View Answer Discuss in Forum

    Percentage increase in area = 2x +
    x²
    		 %
    100

    = 2 × 10 +
    10 × 10
    		 %
    100

    = 21%

    Correct Option: D

    Percentage increase in area = 2x +
    x²
    		 %
    100

    = 2 × 10 +
    10 × 10
    		 %
    100

    = 21%

  1. If the length and breadth of a rectangle are increased by 10% and 8% respectively, then the area of the rectangle increases by :








  1. View Hint View Answer Discuss in Forum

    Percentage increase in area = x + y +
    xy
    		 %
    100

    = 10 + 8 +
    10 × 8
    		 %
    100

    = 18 +
    4
    		 % = 18
    4
    		 %
    55

    Correct Option: B

    Percentage increase in area = x + y +
    xy
    		 %
    100

    = 10 + 8 +
    10 × 8
    		 %
    100

    = 18 +
    4
    		 % = 18
    4
    		 %
    55