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Sample Aptitude Questions of Tata-Steel

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  1. Water is flowing at the rate of 3 km/hr through a circular pipe of 20 cm internal diameter into a circular cistern of diameter 10m and depth 2m. In how much time will the cistern be filled?
    1. l hour
    2. 1 hour 40 minutes
    3. 1 hour 20 minutes
    4. 2 hours 40 minutes
    Answer: Option B.
    Water flowed in 1 hour through the pipe
    =22/7 * 10*10*3000/10000 meter3
    =660/7 meter3
    Volume of circular/cylindrical cistern
    =660/7 * 5*5*2 = 1100/7 meter3
    = Required Time = 1100/7/660/7 = 5/3 hours
    = 1 hour 2/3 * 60 minutes
    = 1 hour 40 minutes
  2. A bicycle wheel makes 5000 revolutions in moving 11 km. The diameter of the wheel, in cm, is
    1. 35
    2. 55
    3. 65
    4. 70
    Answer:  Option D.
    Distance covered by wheel in one revolution = 2Πr
    ∴ 5000 × 2Πr = 11 × 1000
    ⇒ 5000 × 2 × 22/7 × r = 11000
    ⇒ r =11000*7 / 5000*2*22 = 0.35 metre
    = 35 cm
    ∴ Diameter
    = 2 × radius = 2 × 35 = 70 cm

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  1. At each corner of a triangular field of sides 26 m, 28 m and 30 m, a cow is tethered by a rope of, length 7 m. The area (in m2) ungrazed by the cows is
    1. 336
    2. 259
    3. 154
    4. 77
    Answer: Option C.
    Area grazed by all cows 180° / 360 ° Π r 2 = Π r2 = 1/2 * 22/7 *7*7 = 77 sq.metre Semi-perimeter of triangular field(s)
    = 26+28+30 / 2 = 42 metre
    ∴ Area of the field
    √s(s-a)(s-b)(s-c)
    √42(42-26)(42-28)(42-30)
    √42*16*14*12
    = 336 sq. metre
    ∴ Area ungrazed by the cows = 336 - 77 = 259 sq. metre
  2. A shopkeeper allows 23% commission on his advertised price and still makes a profit of 10%. If he gains Rs. 56 on one item, his advertised price of the item, in Rs., is
    1. 820
    2. 780
    3. 790
    4. 800
    Answer: Option D.
    Let the advertised price be Rs. x. ∴ S.P. = Rs. 77x/100
    ∴ C.P. = Rs(77x/100 - 56)
    ⇒ 77x -5600/100 =(100/110 * 77x/100)
    ⇒77x -5600/100 = 7x/10
    ⇒ 7x -5600 = 70x ⇒ 7x = 5600 ⇒ x = Rs. 800
  3. The average of 25 observations is 13. It was later found that an observation 73 was wrongly entered as 48. The new average is
    1. 12.6
    2. 14
    3. 15
    4. 13.8
    Answer: Option B.
    Difference of two observations = 73 - 48 = 25
    ∴ New average = 13 + 25/25 = 14
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  4. If the cost price of 10 articles is equal to the selling price of 8 ar¬ticles, then gain per cent is
    1. 10%
    2. 8%
    3. 50%
    4. 25%
    Answer: Option D.
    Profit percent= 10-8/8 × 100 = 25%
  5. An article is marked 40% above the cost price and a discount of 30% is allowed. What is the gain or loss percentage?
    1. 10% gain
    2. 5% gain
    3. 2% loss
    4. 12% loss
    Answer: Option D.
    Let the C.P. of article be Rs. 100. ∴ Marked price = Rs. 140 S.P. = 70% of 140 = Rs. 98
  6. A man bought oranges at the rate of 8 for Rs. 34 and sold them at the rate of 12 for Rs. 57. How many oranges should be sold to earn a net profit of Rs. 45?
    1. 90
    2. 100
    3. 135
    4. 150
    Answer: Option A
    Let the man buy 24 (LCM of 8 and 12) oranges. ∴ C.P. of 24 oranges = 34/8 × 24 = Rs. 102 S.P. of 24 oranges = 57/12 × 24 = Rs. 114 Gain= 114- 102 = Rs. 12 ∵ Rs. 12≡ 24 oranges ∴ Rs. 45 ≡ 24/12 × 45 = 90 oranges
  7. The number 0.121212.... in the form p/q is equal to
    1. 4/11
    2. 2/11
    3. 4/33
    4. 2/33
    Answer: Option C.
    0.121212 …. = 0.12 = 12/99 =4/33
  8. if(3/5)3 (3/5)-6=(3/5)2x-1 then x is equal to
    1. -2
    2. 2
    3. -1
    4. 1
    Answer: Option C.
    (3/5)3 (3/5)-3 (3/5)-3=(3/5)2x-1
    ⇒(3/5)3 (3/5)-3 (3/5)-3=(3/5)2x-1 ⇒(3/5)0 (3/5)-3=(3/5)2x-1 ⇒ 2x – 1 = - 3 ⇒ 2x = - 3 + 1 = - 2 ⇒ x = - 1

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