Subject

Quantitative Aptitude

Class

SSCCGL Class 12

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 Multiple Choice QuestionsMultiple Choice Questions

104.

Walking 6/7 of his usual speed, a man is 12 min too late. The usual time taken by him to cover that distance is

  • 1 hr

  • 1 h 12 min

  • 1 h 15 min

  • 1 h 20 min


B.

1 h 12 min

New speed  = 6/7 of usual speed.
As speed and time are inversely proportional to each other.
∴   New time = 7/6 of usual time
Now, 
(7/6 of usual time) - (usual time) = 12/60 = 1/5 hr
rightwards double arrow space space 1 over 6 space of space usual space time space equals space 1 fifth
rightwards double arrow space space space space usual space time space space equals space space 6 over 5 space hr space equals space 1 space straight h space 12 space min




54 Views

103.

The cost of an apple is twice that of a banana and the cost of banana is 25% less than that of a guava. If the cost of each type of fruit increases by 10%, then the percentage increase in cost of 4 bananas, 2 apples and 3 guavas is

  • 10%

  • 12%

  • 16%

  • 18%


A.

10%

Let the cost of one banana = ₹ 100
∴       cost of an apple  = ₹ 200
         cost of guava:
                 equals space open parentheses 75 over 100 space equals space 100 space close parentheses
equals space open parentheses fraction numerator 100 space cross times space 100 over denominator 75 end fraction close parentheses space equals space 400 over 3
Total cost of 4 bananas, 2 apples and 3 guavas
     = (4 x 100) + (2 x 200) + (3 x 400/3) = ₹ 1200  ...(i)

After 10% increase in the cost of all fruits
    New cost of banana = ₹ 110
           cost of an apple = 220
            cost of a guava = 440/3

Total cost of 4 bananas, 2 apples and 3 guavas after increase of 10%:
(4 x 110) + (2 x 220) + (3 x 440/3) = ₹ 1320  ...(ii)

From (i) and (ii),
Required percentage increase:
   equals space open parentheses fraction numerator 1320 minus 1200 over denominator 1200 end fraction space cross times space 100 close parentheses
equals space space 10 percent sign



97 Views

101.

A reduction of 20% in the price of an apple enables a man to buy 10 apples more for ₹ 54. The reduced price of apple per dozen is

  • ₹ 4.32

  • ₹ 12.96

  • ₹ 10.80

  • ₹ 14.40


B.

₹ 12.96

Shortcut Method:
    20% of ₹ 54 = 10 apples
    10.8 = 10 apples
   Reduced price per apple:
       equals space open parentheses fraction numerator 10.8 over denominator 10 end fraction close parentheses space equals space ₹ space 1.08
∴  Reduced price per dozen:
    = ₹ 1.08 x 12 = ₹ 12.96

84 Views

109.

A hemisphere and a cone have equal bases. If their heights are also equal, the ratio of their curved surfaces will be

  • 1 space colon square root of 2

  • square root of 2 space colon space 1

  • 1 : 2

  • 2 : 1


B.

square root of 2 space colon space 1

Height of cone = Base radius of hemisphere = r unit.
∴   Slant height of cone (l) = square root of straight h squared space plus space straight r squared end root space equals space square root of 2 space straight r space unit
∴   Required ratio of curved surface area of hemisphere and a cone
                  equals space 2 πr squared space colon space space πrl
equals space 2 space πr squared space colon space πr square root of 2 straight r
equals space 2 space colon space square root of 2
equals space square root of 2 space colon space 1

55 Views

102.

Price of a commodity has increased by 60%. By what percent must a consumer reduce the consumption of the commodity so as not to increase the expenditure?

  • 37

  • 37.5

  • 40.5

  • 60


B.

37.5

Required per cent reduced:
         equals space fraction numerator 60 over denominator left parenthesis 100 space plus space 60 right parenthesis end fraction space cross times space 100 space
equals space 60 over 160 space cross times space 100 space equals space 37.5 percent sign

38 Views

108.

If the difference between SI and CI for 2 yr on a sum of money lent at 5% is ₹ 6, then the sum is

  • ₹ 2200

  • ₹ 2400

  • ₹ 2600

  • ₹ 2000


B.

₹ 2400

Difference space equals space straight P open parentheses straight r over 100 close parentheses squared space space left parenthesis only space for space 2 space yr right parenthesis
rightwards double arrow space space 6 space equals space straight P open parentheses 5 over 100 close parentheses squared
rightwards double arrow space space straight P space equals space fraction numerator 6 space cross times space 100 space cross times space 100 over denominator 5 space cross times space 5 end fraction space equals space ₹ space 2400

39 Views

110.

If straight x space equals space square root of fraction numerator square root of 5 space plus space 1 over denominator square root of 5 minus 1 end fraction end root space then comma the value of 5x2 - 5x - 1 is

  • 0

  • 3

  • 4

  • 5


C.

4

straight x space equals space square root of fraction numerator square root of 5 plus 1 over denominator square root of 5 minus 1 end fraction space cross times space open parentheses fraction numerator square root of 5 plus 1 over denominator square root of 5 plus 1 end fraction close parentheses end root
equals space square root of fraction numerator left parenthesis square root of 5 plus 1 right parenthesis squared over denominator 5 minus 1 end fraction end root space equals space square root of fraction numerator left parenthesis square root of 5 plus 1 right parenthesis squared over denominator 4 end fraction end root
equals space fraction numerator square root of 5 plus 1 over denominator 2 end fraction
∴    5x2 - 5x - 1
      equals space 5 open parentheses fraction numerator square root of 5 plus 1 over denominator 2 end fraction close parentheses squared space minus space 5 open parentheses fraction numerator square root of 5 plus 1 over denominator 2 end fraction close parentheses minus 1
equals space 5 open parentheses fraction numerator 5 plus 1 plus 2 square root of 5 over denominator 4 end fraction close parentheses space minus space open parentheses fraction numerator 5 square root of 2 plus 5 over denominator 2 end fraction close parentheses minus 1
equals space 5 open parentheses fraction numerator 3 plus square root of 5 over denominator 2 end fraction close parentheses space minus space open parentheses fraction numerator 5 square root of 5 plus 5 over denominator 2 end fraction close parentheses minus 1
equals space fraction numerator 15 plus 5 square root of 5 minus 5 square root of 5 minus 5 minus 2 over denominator 2 end fraction space equals space 8 over 2 space equals space 4
   

34 Views

105.

If I walk at 5 km/h, I miss a train by 7 min. If, however, I walk at 6 km/h, I reach the station 5 min before the departure of the train. The distance (in km) between my house and the station is

  • 6

  • 5

  • 4

  • 3


A.

6

Shortcut Method:
   Distance space equals space fraction numerator left parenthesis Product space of space the space Speed right parenthesis over denominator left parenthesis Difference space of space the space speed right parenthesis end fraction space cross times space Difference space in space time
           equals space fraction numerator left parenthesis 5 space cross times space 6 right parenthesis over denominator left parenthesis 6 minus 5 right parenthesis end fraction space cross times space fraction numerator left parenthesis 7 plus 5 right parenthesis over denominator 60 end fraction
equals space 30 space cross times space 1 fifth space equals space 6 space km

34 Views

106.

₹ 800 becomes ₹ 956 in 3 yr at a certain rate of simple interest. If the rate of interest is increased by 4%. What amount will ₹ 800 become in 3 yr?

  • ₹ 1020.80

  • ₹ 1025

  • ₹ 1052

  • ₹ 1050


C.

₹ 1052

Simple interest (SI) for 3yr  = ₹ 956  - ₹ 800 = ₹ 156 
straight S. straight I. space equals space PRT over 100
rightwards double arrow space space 156 space equals space fraction numerator 800 space cross times space straight R space cross times space 3 over denominator 100 end fraction
rightwards double arrow space space straight R space equals space fraction numerator 156 space cross times space 100 over denominator 800 space cross times space 3 end fraction space equals space 6.5
New rate = (6.5 + 4) = 10.5%
Again,
    straight S. straight I. equals space fraction numerator 800 space cross times space 10.5 space cross times space 3 over denominator 100 end fraction equals space ₹ space 252
∴   After 3 yr, amount = 800 + 252 = ₹ 1052

26 Views

107.

Simple interest on a certain sum is 16/25 of the sum. The rate of per cent, if the rate per cent and time (in yr) are equal to

  • 6%

  • 8%

  • 10%

  • 12%


B.

8%

straight S. straight I. space space equals space fraction numerator straight p space cross times space straight r space cross times space straight t over denominator 100 end fraction
                  r = t (given)
therefore space space space 16 over 25 straight p space equals space fraction numerator straight p space cross times space straight r space cross times space straight r over denominator 100 end fraction
rightwards double arrow space space space space straight r squared space equals space 1600 over 25
rightwards double arrow space space space straight r space equals space square root of 1600 over 25 end root
rightwards double arrow space space space straight r space equals space 40 over 5 space equals space 8 percent sign

26 Views