Subject

Quantitative Aptitude

Class

SSCCGL Class 12

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 Multiple Choice QuestionsMultiple Choice Questions

55.

If 3 over 7 straight P space equals space 4 over 11 straight Q comma  then what is the ratio of P and Q respectively?

  • 12 : 77

  • 12 : 33

  • 28 : 33

  • 3 : 28


C.

28 : 33

3 over 7 straight P space equals space 4 over 11 straight Q
rightwards double arrow space space space straight P over straight Q space equals space 4 over 11 space cross times space 7 over 3
rightwards double arrow space space space straight P over straight Q space equals space 28 over 33
rightwards double arrow space space space space straight P space colon thin space thin space straight Q space equals space 28 space colon space 33


52.

A, B and C can complete a work in 20, 24 and 30 days respectively. All three of them starts together but after 4 days A leaves the job and B left the job 6 days before the work was completed. C completed the remaining work alone. In how many days was the total work completed?

  • 10 days

  • 12 days

  • 14 days

  • 16 days


C.

14 days

Shortcut Method:
Let the total work gets completed in 'x' days.
Now,
4 over 20 space plus space fraction numerator straight x minus 6 over denominator 24 end fraction space plus space straight x over 30 space equals space 1
rightwards double arrow space space fraction numerator 6 space cross times space 4 space plus space 5 left parenthesis straight x minus 6 right parenthesis space plus space 4 straight x over denominator 120 end fraction space equals space 1
rightwards double arrow space space space space 24 space plus space 5 straight x space minus space 30 space plus space 4 straight x space equals space 120
rightwards double arrow space space space space space space space space space space space space space 9 straight x space equals space 126
rightwards double arrow space space space space space space space space space space space space straight x space equals space 14 space days


56.

The average of 17 results is 60. If the average of first 9 results is 57 and that of the last 9 results is 65, then what will be the value of 9th result?

  • 39

  • 78

  • 117

  • 156


B.

78

Value of 9th result
                = 9 x 57 + 9 x 65 - 17 x 60
                = 513 + 585 - 1020
                = 1098 - 1020  = 78


53.

A solid sphere of diameter 17.5 cm is cut into two equal halves. What will be the increase (in cm2) in the total surface area?

  • 289 cm2

  • 361.5 cm2

  • 481.25 cm2

  • 962.5 cm2


C.

481.25 cm2

Since the sphere is cut into two equal halves, we will get two hemispheres.
Total Surface area of both hemispheres  = 2 space cross times space 3 πr squared space equals space 6 πr squared
Total Surface area of solid sphere = 4 πr squared
∴  Increase in total surface area equals space 6 πr squared space minus space 4 πr squared space equals space 2 πr squared
           equals space 2 space cross times space 22 over 7 space cross times space open parentheses fraction numerator 17.5 over denominator 2 end fraction close parentheses squared
equals space 481.25 space cm squared


60.

A person lent certain sum of money at 5% per annum simple interest and in 15 years the interest amounted to ₹ 250/- less than the sum lent. What was the sum lent (in ₹)?

  • ₹ 1,000/-

  • ₹ 1,500/-

  • ₹ 2,400/-

  • ₹ 3,000/-


A.

₹ 1,000/-

Let the sum lent be ₹ x.
According to the question,
rightwards double arrow space space space space straight x space minus fraction numerator straight x space cross times space 5 space cross times space 15 over denominator 100 end fraction space equals space 250
rightwards double arrow space space 100 straight x space minus space 75 straight x space equals space 250 space cross times space 100
rightwards double arrow space space space space space space space 25 straight x space equals space 250 space cross times space 100
rightwards double arrow space space space space space space space space space space space space space space straight x space equals space ₹ space 1 comma 000 divided by negative
space space space space


59.

A boat goes 15 upstream and 10 1 half km downstream in 3 hours 15 minutes. It goes 12 km upstream and 14  km downstream in 3 hours. What is the speed of boat in still water.

  • 4 km/hr

  • 6 km/hr

  • 10 km/h

  • 14 km/hr


C.

10 km/h

Let speed of boat with downstream = x km/hr.
      speed of boat with upstream = y km/hr.
According to the question,
  fraction numerator 21 over denominator 2 straight x end fraction space plus space 15 over straight y space equals space 3 1 fourth space equals space 13 over 4 space space space space space space space space space space space space space... left parenthesis straight i right parenthesis
14 over straight x space plus space 12 over straight y space equals space 3 space space space space space space space space space space space space space space space space space space space space space space space space space... left parenthesis ii right parenthesis
Solving (i) and (ii), we get
  x = 14,  y = 6
∴  Speed of boat in still water

equals space 1 half left parenthesis straight x space plus space straight y right parenthesis space equals space 1 half left parenthesis 14 space plus space 6 right parenthesis space equals space 20 over 2 space equals space 10 space km divided by hr.
                 




54.

After a discount of 34% an article is sold for ₹ 3,168/-. What is the marked price (in ₹) of the article?

  • ₹ 4,750/-

  • ₹ 4,800/-

  • ₹ 4,850/-

  • ₹ 5,000/-


B.

₹ 4,800/-

Shortcut Method:
straight M. straight P. space equals space ₹ space 3168 space cross times space fraction numerator 100 over denominator left parenthesis 100 minus 34 right parenthesis end fraction
space space space space space space equals space ₹ space 3168 space cross times space 100 over 66 space equals space ₹ space 4800 divided by negative


58.

32% of a number exceeds 17% of the same number by 120. What is the value of the number?

  • 900

  • 860

  • 940

  • 800


D.

800

Let the number be x.
According to the question,
     rightwards double arrow space space space space space straight x space cross times space 32 over 100 space minus space straight x space cross times space 17 over 100 space equals space 120
rightwards double arrow space space space space space space space space space space space space space fraction numerator 15 straight x over denominator 100 end fraction space equals space 120 space space space rightwards double arrow space space space straight x space equals space 800


57.

For an article the profit is 170% of the cost price. If the cost price increases by 20% but the selling price remains same, then what is the new profit percentage?

  • 41%

  • 50%

  • 75%

  • 125%


D.

125%

Let the C.P. be ₹ 100.
Profit space equals space 170 over 100 space cross times space 100 space equals space 170
S.P. = ₹ (100 + 170) = ₹ 270
Now, If C.P. is increased by 20%
∴    New C.P. =  ₹ 120,  S.P is same i.e.  = ₹ 270
therefore space space space Profit percent sign space equals space fraction numerator 270 minus 120 over denominator 120 end fraction space cross times space 100
space equals space 150 over 6 space cross times space 5 space equals space 125 percent sign



51.

If X and Y are the two digits of the number 347XY such that the number is completely divisible by 80, then what is the value of X + Y?

  • 2

  • 4

  • 6

  • 8


A.

2

If 347XY is divisible by 80 (i.e. 8 x 10), then Y = 0 is the only possibility.
A number is divisible by 8, if its last three digits are divisible by 8.
Last 3 digits i.e. 7X0 should be divisible by 8
So, X = 2
∴   X + Y = 2 + 0 = 2