Subject

Quantitative Aptitude

Class

SSCCGL Class 12

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 Multiple Choice QuestionsMultiple Choice Questions

107.

On decreasing each side of an equilateral triangle by 2cm, there is a decrease of 4 square root of 3 space cm squared in its area. The length of each side of the triangle is

  • 3 cm

  • 5 cm

  • 6 cm

  • 8 cm


B.

5 cm

Let each side of an equilateral triangle be x.
therefore  Area of equilateral triangle = fraction numerator square root of 3 over denominator 4 end fraction straight x squared
On decreasing each side of an equilateral triangle by 2 cm. Then,
new side  = (x - 2) cm

therefore Area of equilateral triangle  = fraction numerator square root of 3 over denominator 4 end fraction left parenthesis straight x minus 2 right parenthesis squared
  According to the question,
                     fraction numerator square root of 3 over denominator 4 end fraction straight x squared space minus space fraction numerator square root of 3 over denominator 4 end fraction left parenthesis straight x minus 2 right parenthesis squared space equals space 4 square root of 3
rightwards double arrow space space fraction numerator square root of 3 over denominator 4 end fraction left square bracket straight x squared minus left parenthesis straight x squared minus 4 straight x plus 4 right parenthesis right square bracket space equals space 4 square root of 3
rightwards double arrow   fraction numerator square root of 3 over denominator 4 end fraction left parenthesis straight x squared minus straight x squared plus 4 straight x minus 4 right parenthesis space equals space 4 square root of 3
rightwards double arrow                fraction numerator square root of 3 over denominator 4 end fraction left parenthesis 4 straight x minus 4 right parenthesis space equals space 4 square root of 3
    rightwards double arrow            4 straight x minus 4 space equals space 16 space rightwards double arrow space space space 4 straight x space equals space 20
    rightwards double arrow             x =  5 cm
Hence, the length of each side is 5 cm.

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104.

P can do a piece of work in 9 days. Q is 50% more efficient than P. The number of days it takes for Q to do the same piece of work is

  • 13 1 half
  • 4 1 half
  • 6

  • 3


C.

6

As per question if Q is 50% more efficient than P,
and let's suppose Q takes 100 days then P would be taking 150 days.
So, the required ratio would be
P      :   Q     :: 9 : x
150  :   100  :: 9 : x
rightwards double arrow space straight x space equals space fraction numerator 100 space cross times space 9 over denominator 150 end fraction
rightwards double arrow space space straight x space equals space 6 space days 

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109.

A merchant advertise 10% off on the items bought from his store. The total discount got by a customer who bought a cooker worth ₹ 650, a heater worth ₹ 500 and a bag worth ₹ 65 is

  • ₹ 120.50

  • ₹ 123.50

  • ₹ 128.50

  • ₹ 121.50


D.

₹ 121.50

Here, cost of a cooker  = ₹ 650
         cost of a heater  = ₹ 500
and cost of a  bag = ₹ 65
Total cost  = ₹(650+500+65)
                = ₹ 1215
Discount = 10%
Hence, the total discount  = ₹ (10% of 1215)          
                                      = ₹ 121.50

               

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101.

The least prime number is

  • 0

  • 1

  • 3

  • 2


D.

2

A natural number other than 1,  is a prime number if and only if it is divisible by 1 and the number itself.
Thus, the least prime number is 2.

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108.

A rectangular tin sheet is 12 cm long and 5 cm broad. It is rolled along its length to form a cylinder by making the opposite edges just to touch each other. Then, the volume of the cylinder is

  • 180 over straight picm3
  • 120 over straight pi cm cubed
  • 100 over straight pi cm cubed
  • 60 over straight pi cm cubed

A.

180 over straight picm3

Here, length of the rectangular tin sheet  = 12 cm
and breadth of the rectangular tin sheet  = 5 cm
When the rectangular sheet is rolled along its length into a cylinder so that the width of the sheet becomes the height of the cylinder, then the length of the sheet equals the circumference of the base of the cylinder.
 i.e.,     2 πr space equals space 12
                        straight r space equals space fraction numerator 12 over denominator 2 straight pi end fraction space equals space 6 over straight pi cm
and height,  h = 5 cm
therefore Volume of the cylinder  = πr squared straight h
                equals space straight pi open parentheses 6 over straight pi close parentheses squared cross times 5 space equals space straight pi cross times 36 over straight pi squared cross times 5
                                 equals 180 over straight pi cm cubed

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105.

16 men can complete a work in 15 days, 24 children can do the same work in 20 days. In how many days will 8 men and 8 children, complete the same work?

  • 16

  • 13 1 third
  • 20

  • 18


C.

20

Use the trick, P. D. = P. D.  (i.e. person x days  = person x days)
                 16 m x 15 d  = 24 c x 20 d
                              3 m = 6 c
                        rightwards double arrow  1 m = 2 c
Now,
     8 children  = 4 men
So,
     (8M + 4M) x X days  = 16 M x 15 days
       rightwards double arrow       X = 20 days

 

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102.

Find the least number which when divided by 12, 18, 36 and 45 leaves the remainder 8, 14, 32 and 41 respectively.

  • 176

  • 180

  • 178

  • 186


A.

176

Here, 12 - 8 = 4
         18 - 14 = 4
         36 - 32 = 4
         45 - 41 = 4

therefore The required number
     = (LCM of 12, 18, 36 and 45) - 4
     
L.C.M. = 2 x 2 x 3 x 3 x 5 = 180
The required number  = 180 - 4 = 176



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110.

What is a better investment, 4% stock at ₹ 120 or  3% stock at ₹ 80?

  • First

  • Second

  • Both

  • None of these


A.

First

4% stock at ₹ 120 = 4% of 120
                         equals space 4 over 100 cross times 120 space equals ₹ space 4.80
and 3% stock at ₹ 80 = 3% of 80
                                equals 3 over 100 cross times 80
                                = ₹ 2.40
It is clear that first investment is better. 

215 Views

106.

The area of the iron sheet required to prepare a cone 24 cm high with base radius 7 cm is open parentheses Take space straight pi space equals space 22 over 7 close parentheses.

  • 708 cm2

  • 804 cm2

  • 704 cm2

  • 408 cm2


C.

704 cm2

Here, height of a cone  (h) = 24 cm
 Radius of the base, r = 7 cm
 therefore  Slant height straight l space equals space square root of straight r squared plus straight h squared end root
                        space equals space square root of 24 squared plus 7 squared end root space equals space square root of 576 plus 49 end root
equals space square root of 625 space equals space 25 space cm
therefore  Area of the iron sheet = Total surface area of the cone
                              equals space πrl plus πr squared space equals space πr left parenthesis straight l plus straight r right parenthesis
equals 22 over 7 cross times 7 left parenthesis 25 plus 7 right parenthesis
equals space 22 space cross times space 32 space equals space 704 space cm squared

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103.

An empty pool being filled with water at a constant rate takes 8h to fill 3 over 5 th of its capacity. How much more time will it take to finish filling the pool?

  • 5 h 30 min

  • 5 h 20 min

  • 4 h 48 min

  • 4 h 50 min


B.

5 h 20 min

Time taken to fill the 3 over 5 th part of a pool = 8 h
Remaining part  = open parentheses 1 minus 3 over 5 close parentheses
                      equals space 2 over 5 th

therefore  Time taken to fill the 2 over 5 th part of a pool
                            equals space fraction numerator 8 cross times 2 cross times 5 over denominator 5 cross times 3 end fraction space equals space 16 over 3
                            equals space 5 1 third straight h = 5 h 20 min

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