Subject

Quantitative Aptitude

Class

SSCCGL Class 12

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 Multiple Choice QuestionsMultiple Choice Questions

53.

The numbers x, y, z are respectively proportional to 2 : 3 : 5 and the sum of x, y and z is 80. If the number z is given by the equation z = ax - 8, then a is

  • 6

  • 3 over 2

  • 3

  • 5 over 2


C.

3

x : y : z = 2 : 3 : 5
x + y + z = 80
straight x space equals space 80 space cross times space 2 over 10 space equals space 16
straight y space equals space 80 space cross times 3 over 10 space equals space 24
straight z space equals space 80 space cross times space 5 over 10 space equals space 40
z = ax - 8
rightwards double arrow space space 40 space equals space straight a space cross times space 16 space minus space 8
rightwards double arrow space space 16 straight a space equals space 48
rightwards double arrow space space straight a space equals space 3

 

 

 

 

92 Views

51.

A is twice as good as B and together they finish a piece of work in 16 days. The number of days taken by A alone to finish the work in

  • 20 days

  • 21 days

  • 22 days

  • 24 days


D.

24 days

Let A finishes the work in x days.
      ∴   B finishes the work in 2x days. 
According to the question,
 Both will finish in open parentheses fraction numerator straight A space cross times straight B over denominator straight A plus straight B end fraction close parentheses = 16 days
therefore space space space fraction numerator straight x space cross times space 2 straight x over denominator 3 straight x end fraction space equals space 16
rightwards double arrow space space space fraction numerator 2 straight x squared over denominator 3 straight x end fraction space equals space 16
rightwards double arrow space space space straight x space equals space 24 space days

       

 

 

 

 

110 Views

59.

When 2 straight x plus 2 over straight x space equals space 3 comma then value of straight x cubed space plus space 1 over straight x cubed plus 2 is

  • 2 over 7

  • 7 over 8

  • 7 over 2

  • 8 over 7


B.

7 over 8

2 straight x space plus space 2 over straight x space equals space 3
rightwards double arrow space space straight x space plus space 1 over straight x space equals space 3 over 2
rightwards double arrow space open parentheses straight x space plus space 1 over straight x close parentheses cubed space equals space open parentheses 3 over 2 close parentheses cubed
rightwards double arrow space space straight x cubed space plus space 1 over straight x cubed space plus space 3 straight x space cross times space 1 over straight x open parentheses straight x plus 1 over straight x close parentheses space equals 27 over 8
rightwards double arrow space space space straight x cubed space plus space 1 over straight x cubed space plus space 3 space cross times space 3 over 2 space equals space 27 over 8
rightwards double arrow space space straight x cubed space plus space 1 over straight x cubed space plus space 2 space equals space 27 over 8 minus 9 over 2 plus 2

rightwards double arrow space straight x cubed space plus space 1 over straight x cubed space plus 2 space equals space fraction numerator 27 minus 36 plus 16 over denominator 8 end fraction
rightwards double arrow space space straight x cubed plus 1 over straight x cubed plus 2 space equals space 7 over 8

 

 

54 Views

56.

A man covers a total distance of 100 km on bicycle. For the first 2 hours, the speed was 20 km/hr and for the rest of the journey, it came down to 10 km/hr. The average speed will be

  • 12 1 half space km divided by hr

  • 13 km/hr

  • 15 1 over 8 space km divided by hr

  • 20 km/hr


A.

12 1 half space km divided by hr

Distance covered by man in first 2 hours = 2 x 20 = 40 km
Remaining distance  = (100 - 40) = 60 km
Time to cover this 60 km with speed of 10 km/hr
open parentheses 60 over 10 close parentheses km divided by hr space equals space 6 space hours
Required Average speed = open parentheses fraction numerator Total space Distance over denominator Total space Time space Taken end fraction close parentheses
                                 equals space open parentheses fraction numerator 100 over denominator 2 plus 6 end fraction close parentheses space equals space open parentheses 100 over 8 close parentheses space equals space 12 1 half space km divided by hr
                     
              

 

142 Views

57.

Alipta got some amount of money from her father. In how many years will the ratio of the money and the interest obtained from it be 10 : 3 at 6% simple interest per annum?

  • 7 years

  • 3 years

  • 5 years

  • 4 years


C.

5 years

Let the required time be t years.
According to the question,
3 space equals space fraction numerator 10 space cross times space straight t space cross times space 6 over denominator 100 end fraction
straight t space equals space 5 space years

106 Views

58.

If (x - 2) (x - p) = x2 - ax + 6, then the value of (a - p) is:

  • 0

  • 1

  • 2

  • 3


C.

2

(x - 2) (x - p) = x2 - ax + 6
x2 - 2x - px + 2p = x2 - ax + 6
x2 - x(2 + p) + 2p = x2 - ax + 6
Comparing both sides,
      2 + p = a
       a - p = 2

78 Views

52.

The successive discounts of 15%, 20% and 25% on an article is equivalent to the single discount of

  • 60%

  • 47%

  • 49%

  • 40%


C.

49%

Single discount of 15% and 20%
             equals space 15 space plus space 20 space minus space fraction numerator 15 space cross times space 20 over denominator 100 end fraction
equals space 32 percent sign

Single discount of 32% and 25%
             equals space 32 space plus space 25 space minus space fraction numerator 32 space cross times space 25 over denominator 100 end fraction
equals space 49 percent sign

 

90 Views

54.

If the ratio of cost price and selling price be 10 : 11, then the profit percentage is

  • 1%

  • 10%

  • 5%

  • 8%


B.

10%

Let the cost price be Rs. 10,   Selling price be Rs. 11
∴  Gain  = Rs. (11 - 10) = Rs. 1
  Gain%
   equals space open parentheses fraction numerator Gain over denominator straight C. straight P. end fraction space cross times space 100 close parentheses
equals space open parentheses 1 over 10 space cross times space 100 close parentheses
equals space 10 percent sign

 

62 Views

55.

The price of rice has increased by 60%. In order to restore the original price, the new price must be reduced by:

  • 33 1 third percent sign

  • 37 1 half percent sign

  • 40%

  • 45%


B.

37 1 half percent sign

New price must be reduced by:
   equals space open parentheses fraction numerator 60 over denominator 100 plus 60 end fraction cross times space 100 close parentheses
equals space open parentheses 60 over 160 cross times space 100 close parentheses space equals space 37.5 percent sign

74 Views

60.

In a triangle ABC, if angle straight A space space plus space angle straight C space equals space 140 degree and angle straight A space plus space 3 angle straight B space equals space 180 degree, then angle straight A is equal to

  • 80°

  • 40°

  • 60°

  • 20°


C.

60°

angle straight A space plus space angle straight C space equals space 140 degree
space space space space space angle straight C space equals space 140 degree space minus space angle straight A space space space space... left parenthesis straight i right parenthesis


angle straight A space plus space 3 angle straight B space equals space 180 degree
angle straight B space equals space fraction numerator 180 degree space minus space angle straight A over denominator 3 end fraction space space space... left parenthesis ii right parenthesis

From (i) and (ii), 
angle straight A space plus space angle straight B space plus space angle straight C space equals space 180 degree
angle straight A space plus space fraction numerator 180 degree space minus space angle straight A over denominator 3 end fraction space plus space 140 degree space minus space angle straight A space equals space 180 degree
fraction numerator 3 angle straight A plus 180 degree space minus space angle straight A minus 3 angle straight A over denominator 3 end fraction space equals space 180 degree space minus space 140 degree
fraction numerator 180 degree space minus space angle straight A over denominator 3 end fraction space equals space 40 degree space space space space space space space space space space space


rightwards double arrow space space 180 degree space minus space angle straight A space equals space 120 degree
rightwards double arrow space space space space space space space space angle straight A space equals space 180 degree space minus space 120 degree
rightwards double arrow space space space space space space angle straight A space equals space 60 degree

 

 

 

60 Views