11. The angle between the minute hand and hour hand of a clock when the time is 7 : 20 is equal to
    

1. 1. 45°
      

   
   
   

   2. 90°
      

   
   
   

   3. 100°
      

   
   
   

   4. 120°

   
   
   

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1. View Hint View Answer Discuss in Forum

   As per the given in question ,
   

   At 7 : 20, Number of hours = 7	20	= 7	1	hours
   	60		3

   
   

   Number of hours =	22	hours
   	3

   
   The hour–hand traces 360° in 12 hours.
   

   ∴ Angle traced by hour hand in 22/3 hours =	360°	×	22	= 220°
   	12		3

   
   

   Correct Option: C

   As per the given in question ,
   

   At 7 : 20, Number of hours = 7	20	= 7	1	hours
   	60		3

   
   

   Number of hours =	22	hours
   	3

   
   The hour–hand traces 360° in 12 hours.
   

   ∴ Angle traced by hour hand in 22/3 hours =	360°	×	22	= 220°
   	12		3

   
   ∵ Minute hand traces 360° in 60 minutes.
   

   ∴ Angle traced by minute hand in 20 minutes =	360°	× 20 = 120°
   	60

   
   ∴ Required angle = 220° – 120° = 100°

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12. If a machine consumes k/5 kilo watts of power every t hours, how much power in kilowatts, will three such machines consume in 10 hours ?

1. 1. k

      t

   
   
   

   2. 6t

      k

   
   
   

   3. 6k

      t

   
   
   

   4. t

      k

   
   
   

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1. View Hint View Answer Discuss in Forum

   From the question ,
   

   Power consumed by each machine in 10 hours =	k × 10	=	2k	kilowatts
   	5 × t		t

   
   

   Correct Option: C

   From the question ,
   

   Power consumed by each machine in 10 hours =	k × 10	=	2k	kilowatts
   	5 × t		t

   
   

   ∴ Power consumed by three such machines = 3 ×	2k	=	6k	kilowatts
   	t		t

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13. A box weighs 8.5 kg when full of sand and weighs 5.5 kg when it is half filled with sand. The weight of the empty box is :
    

1. 1. 5 kg.
      

   
   
   

   2. 6 kg.
      

   
   
   

   3. 2.5 kg.
      

   
   
   

   4. 4.5 kg.

   
   
   

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1. View Hint View Answer Discuss in Forum

   According to the question,
   Box + 1 part sand = 8.5 kg.
   

   Box +	1	filled sand = 5.5 kg.
   	2

   
   On subtracting of both equations , we get
   

   Weight of	1	filled sand = 8.5 - 5.5 = 3 kg.
   	2

   
   

   Correct Option: C

   According to the question,
   Box + 1 part sand = 8.5 kg.
   

   Box +	1	filled sand = 5.5 kg.
   	2

   
   On subtracting of both equations , we get
   

   Weight of	1	filled sand = 8.5 - 5.5 = 3 kg.
   	2

   
   ∴ Weight of 1 part sand = 6 kg.
   ∴ Weight of empty box = (8.5 – 6) kg. = 2.5 kg.

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14. A man having height 169 cm is standing near a pole. He casts a shadow 130 cm long. What is the length of the pole if it gives a shadow 420 cm long ?
    

1. 1. 550 cm
      

   
   
   

   2. 589 cm
      

   
   
   

   3. 323 cm
      

   
   
   

   4. 546 cm

   
   
   

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1. View Hint View Answer Discuss in Forum

   Given that , Height of man = 169 cm
   Length of shadow of the pole = 420 cm
   Length of shadow of man = 130 cm
   

   ∴	Height of man	=	Length of shadow of man
   	Height of pole		Length of shadow of pole

   
   

   ⇒	169	=	130
   	Height of pole		420

   
   

   Correct Option: D

   Given that , Height of man = 169 cm
   Length of shadow of the pole = 420 cm
   Length of shadow of man = 130 cm
   

   ∴	Height of man	=	Length of shadow of man
   	Height of pole		Length of shadow of pole

   
   

   ⇒	169	=	130
   	Height of pole		420

   
   ⇒ Height of pole × 130 = 169 × 420
   

   ⇒ Height of pole =	169 × 420	= 546 cm
   	130

   
   

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15. 11 friends went to a hotel and decided to pay the bill amount equally. But 10 of them could pay 60 each, as a result 11th has to pay 50 extra than his share. Find the amount paid by him.
    

1. 1. 105
      

   
   
   

   2. 110
      

   
   
   

   3. 115
      

   
   
   

   4. 120

   
   
   

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1. View Hint View Answer Discuss in Forum

   Suppose Total bill = Rs. p
   

   ∴ 10 × 60 +	p	+ 50 = p
   	11

   
   

   ⇒ 600 + 50 +	p	= p
   	11

   
   

   ⇒ p -	p	= 650
   	11

   
   

   ⇒	11p - p	= 650
   	11

   
   ⇒ 10p = 650 × 11
   ⇒ p = 65 × 11 = 715
   

   Correct Option: C

   Suppose Total bill = Rs. p
   

   ∴ 10 × 60 +	p	+ 50 = p
   	11

   
   

   ⇒ 600 + 50 +	p	= p
   	11

   
   

   ⇒ p -	p	= 650
   	11

   
   

   ⇒	11p - p	= 650
   	11

   
   ⇒ 10p = 650 × 11
   ⇒ p = 65 × 11 = 715
   

   ∴ Amount paid by the eleventh person =	p	+ 50 = Rs.		750	+ 50
   	11			11

   
   Hence , Amount paid by the eleventh person = Rs. (65 + 50) = Rs. 115

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