Subject

Quantitative Aptitude

Class

SSCCGL Class 12

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 Multiple Choice QuestionsMultiple Choice Questions

53.

If the ratio of two numbers is 1 : 5 and their product is 320, then the difference between the square of these two numbers is

  • 1024

  • 1256

  • 1536

  • 1435


C.

1536

Let the numbers be x and 5x respectively.
According to the question,
   straight x space cross times space 5 straight x space equals space 320
rightwards double arrow space space 5 straight x squared space equals space 320
rightwards double arrow space space straight x squared space equals space 320 over 5 space equals space 64 space rightwards double arrow space space straight x space equals space 8
∴   Difference between the squares of these two numbers
      = (5 x 8)2 - (8)2 = 1600 - 64 = 1536

65 Views

60.

If left parenthesis straight a minus 2 right parenthesis space plus space fraction numerator 1 over denominator left parenthesis straight a space plus space 2 right parenthesis end fraction space equals space minus 1, then the value of left parenthesis straight a plus 2 right parenthesis squared space plus space fraction numerator 1 over denominator left parenthesis straight a plus 2 right parenthesis squared end fraction is

  • 7

  • 11

  • 23

  • 27


A.

7

left parenthesis straight a minus 2 right parenthesis space plus space fraction numerator 1 over denominator left parenthesis straight a plus 2 right parenthesis end fraction space equals space minus 1
rightwards double arrow space space straight a space minus space 2 space plus space 4 space plus space fraction numerator 1 over denominator straight a plus 2 end fraction space equals space 4 minus space 1
rightwards double arrow space space space straight a space plus space 2 space plus space fraction numerator 1 over denominator straight a plus 2 end fraction space equals space 3
S.B.S.
rightwards double arrow space space left parenthesis straight a space plus space 2 right parenthesis squared space plus space fraction numerator 1 over denominator left parenthesis straight a plus 2 right parenthesis squared end fraction space plus space 2 space equals space 9
rightwards double arrow space space space left parenthesis straight a space plus space 2 right parenthesis squared space plus space fraction numerator 1 over denominator left parenthesis straight a plus 2 right parenthesis squared end fraction space equals space 9 space minus space 2
rightwards double arrow space space space left parenthesis straight a space plus space 2 right parenthesis squared space plus space fraction numerator 1 over denominator left parenthesis straight a plus 2 right parenthesis squared end fraction space equals space 7

40 Views

56.

x is 5 times longer than y. The percentage by which y is less than x is

  • 50%

  • 40%

  • 80%

  • 70%


C.

80%

x = 5y
straight x over straight y space equals space fraction numerator begin display style 5 end style over denominator 1 end fraction space
straight x space colon space straight y space equals space 5 space colon thin space 1
∴  Required percentage
    space equals space fraction numerator left parenthesis 5 minus 1 right parenthesis over denominator 5 end fraction space cross times space 100 space equals space 80 percent sign

70 Views

52.

The rate of discount being given on a shirt, where selling price is Rs. 546 after deducting a discount of Rs. 109/- on its marked price is

  • 14%

  • 18%

  • 15%

  • 16%


D.

16%

Selling price =  Rs. 546
Discount  = Rs. 109
Marked price = Rs. (546 + 109) = Rs. 655
Now, 
Let x be the discount % on M.P.
  therefore space space 655 space cross times space straight x over 100 space equals space 109
rightwards double arrow space space space straight x space equals space space fraction numerator 109 space cross times space 100 over denominator 655 end fraction space equals space 16.64 space almost equal to space 16 percent sign

44 Views

55.

A man bought 30 defective machines for Rs. 1,000/-. He repaired and sold them at the rate of Rs. 300 per machine. He got profit of Rs. 150 per machine. How much did he spend on repairs? (in Rs)

  • Rs 5,500

  • Rs 4,500

  • Rs 3,500

  • Rs 2,500


C.

Rs 3,500

Cost of one machine  = open parentheses 1000 over 30 close parentheses space equals 100 over 3 space equals space Rs. space 33.33
Profit on one machine = Rs. 150
Selling price of one machine = Rs 300
Repairing cost of one machine = 300 - 150 - 33.33 = Rs. 116.67
∴  Total amount spent on repairing 
                                   = Rs. 116.67 x 30 = Rs. 3,500/-

59 Views

57.

A motor cycle gives an average of 45 km per litre. If the cost of petrol is Rs. 20 per litre. The amount required to complete journey of 540 km is (in Rs):

  • Rs. 120/-

  • Rs. 360/-

  • Rs. 200/-

  • Rs. 240/-


D.

Rs. 240/-

Amount required to complete a journey of 540 km
                   equals space 540 over 45 space cross times space 20 space equals space Rs. space 240

51 Views

58.

A sum of money amounts to Rs 6,655/- at the rate of 10% compounded annually for 3 years. The sum of money is:

  • Rs 5,000

  • Rs 5,500

  • Rs 6,000

  • Rs 6,100


A.

Rs 5,000

straight A space equals space straight P open parentheses 1 plus straight r over 100 close parentheses to the power of straight n
rightwards double arrow space space space 6655 space equals space straight P open square brackets 1 plus 10 over 100 close square brackets cubed
rightwards double arrow space space 6655 space equals space straight P open square brackets 11 over 10 close square brackets cubed
rightwards double arrow space space 6655 space equals space straight P space cross times space 1331 over 1000
rightwards double arrow space space space straight P space equals space Rs space 5 comma 000

70 Views

54.

Number of boys and girls are 'x' and 'y' respectively; ages of a girl and a boy are 'a' years and 'b' years respectively. The average age (in years) of all boys and girls is

  • fraction numerator straight x space plus space straight y over denominator bx space plus space ay end fraction

  • fraction numerator bx plus ay over denominator straight x plus straight y end fraction

  • fraction numerator ax plus by over denominator straight x plus straight y end fraction

  • fraction numerator straight x plus straight y over denominator ax plus by end fraction


B.

fraction numerator bx plus ay over denominator straight x plus straight y end fraction

Total age of all boys = bx
Total age of all girls  = ay
∴  Average age of all boys and girls:
                     equals space fraction numerator bx plus ay over denominator straight x plus straight y end fraction

53 Views

59.

If x2 - 4x + 1 = 0,   the value of fraction numerator straight x to the power of 6 plus 1 over denominator straight x cubed end fraction space is:

  • 48

  • 52

  • 55

  • 58


B.

52

x2 - 4x + 1 = 0
straight x squared minus 4 straight x plus 1 space equals space 0
rightwards double arrow space space straight x squared plus 1 space equals space 4 straight x
rightwards double arrow space space space straight x plus space 1 over straight x space equals space 4
If straight x space plus space 1 over straight x space equals space straight a comma   then straight x cubed space plus space 1 over straight x cubed space equals space straight a cubed space minus space 3 straight a
therefore space space straight x cubed space plus space 1 over straight x cubed space equals space left parenthesis 4 right parenthesis cubed space minus space 3 space cross times space 4 space equals space 64 space minus space 12 space equals space 52
therefore space space straight x cubed space plus space 1 over straight x cubed space equals space fraction numerator straight x to the power of 6 plus 1 over denominator straight x cubed end fraction space equals space 52


45 Views

51.

If 4 over 5 th of a number exceeds its 3 over 4 th by 8, then the number is:

  • 130

  • 120

  • 160

  • 150


C.

160

Let the number be x.
According to the question,
     rightwards double arrow space space 4 over 5 straight x space minus space 3 over 4 straight x space equals space 8
rightwards double arrow space space fraction numerator 16 straight x minus 15 straight x over denominator 20 end fraction space equals space 8
rightwards double arrow space space space space space space space space straight x space equals space 160

103 Views