1.  Three-fourth of a number is equal to 60% of another number. What is the difference between the numbers?

a

  18

b

  32

c

  24

d

  Cannot be determined

e

  None of these

Answer & Explanation
Answer : Option D
Explanation :

Let the numbers be x and y respectively. Then,

34x=60%  of  y\frac{3}{4}x = 60{\rm{\% \;of\;}}y

34x=60100y \Rightarrow \frac{3}{4}x = \frac{{60}}{{100}}y

34x=35y \Rightarrow \frac{3}{4}x = \frac{3}{5}y

y=34×53x=54x \Rightarrow y = \frac{3}{4} \times \frac{5}{3}x = \frac{5}{4}x

yx\therefore y - x

=54xx=x4 = \frac{5}{4}x - x = \frac{x}{4}

Clearly, no unique answer is possible.

2.  Abhijit invested in three schemes A, B and C the amounts in the ratio of 2 : 3 : 4 respectively. If the schemes offered interest @ 20 p.c.p.a. 16 p.c.p.a. and 15 p.c.p.a. respectively, what will be the respective ratio of the amounts after one year ?

a

  10 : 8 : 5

b

  12 : 14 : 15

c

  12 : 15 : 22

d

  Cannot be determined

e

  None of these

Answer & Explanation
Answer : Option E
Explanation :

Let Abhijit invested Rs. 2x, Rs. 3x and Rs. 4x in three schemes A, B and C respectively.

\therefore The required ratio

=2x×120100:3x×116100:4x×115100 = 2x \times \frac{{120}}{{100}}:3x \times \frac{{116}}{{100}}:4x \times \frac{{115}}{{100}}

=2×120:3×116:4×115 = 2 \times 120:3 \times 116:4 \times 115

=60:87:115 = 60:87:115

3.  A train crosses a 300 metre long platform in 38 seconds while it crosses a signal pole in 18 seconds. What is the speed of the train in kmph ?

a

  Cannot be determined

b

  72

c

  48

d

  54

e

  None of these

Answer & Explanation
Answer : Option D
Explanation :

54

4.  If 2x + 5y = 109 and 2x + 5 = y + 12 then y x = ?

a

  7

b

  6

c

  8

d

  9

e

  None of these

Answer & Explanation
Answer : Option E
Explanation :

2x + 5y = 109 .....(i)

2x + 5 = y + 12

2x y = 12 – 5

2x y = 7 .....(ii)

On subtracting equation (ii) from (i),

2x + 5y – (2x y) = 109 – 7

2x + 5y – 2x + y = 102

\Rightarrow 6y = 102

\Rightarrow y = 1026=17\frac{{102}}{6} = 17

From equation (ii),

2x – 17 = 7

2x = 24

x = 12

y x = 17 – 12 = 5

5.  Four of the following five parts are exactly equal. The number of the part, which is not equal to the other four parts, is your answer.

a

  45 × 12 + 60

b

  80% of 800 – 40

c

   35  of  1200150{\rm{\;}}\frac{3}{5}{\rm{\;of\;}}1200 - 150

d

  1260 ÷ 3 ÷ 180

e

  8640 ÷ 16 + 60

Answer & Explanation
Answer : Option C
Explanation :

[1] \to 45 × 12 + 60 = 540 + 60 = 600

[2] \to 80% of 800 – 40 =80×80010040 = \frac{{80 \times 800}}{{100}} - 40 = 640 – 40 = 600

[3] \to 35\frac{3}{5} of 1200 – 150 = 35\frac{3}{5} ×1200 – 150 = 720 – 150 = 570

[4] \to 12603\frac{{1260}}{3} +180 = 420 + 180 = 600

[5] \to 864016\frac{{8640}}{{16}} + 60 = 540 + 60 = 600

6.  Certain number of pieces of an article are to be packed in boxes, such that each box contains 145 pieces. If after packing them in 32 boxes 25 pieces are left out, what was the number of pieces to be packed ?

a

  4566

b

  4655

c

  4465

d

  4640

e

  None of these

Answer & Explanation
Answer : Option E
Explanation :

Number of pieces

= 32 × 145 + 25

= 4640 + 25 = 4665

7.  Which of the following set of fractions is in ascending order ?

a

  1315,1113,78,89\frac{{13}}{{15}},\frac{{11}}{{13}},\frac{7}{8},\frac{8}{9}

b

  1113,1315,78,89\frac{{11}}{{13}},\frac{{13}}{{15}},\frac{7}{8},\frac{8}{9}

c

  89,78,1315,1113\frac{8}{9},\frac{7}{8},\frac{{13}}{{15}},\frac{{11}}{{13}}

d

  78,89,1113,1315\frac{7}{8},\frac{8}{9},\frac{{11}}{{13}},\frac{{13}}{{15}}

e

  None of these

Answer & Explanation
Answer : Option B
Explanation :

Decimal equivalent of :

1315=0.87\frac{{13}}{{15}} = 0.87

1113=0.85\frac{{11}}{{13}} = 0.85

78=0.875\frac{7}{8} = 0.875

89=0.89\frac{8}{9} = 0.89

Clearly,

0.85 < 0.87 < 0.875 < 0.89

1113<1315<78<89\therefore \frac{{11}}{{13}} < \frac{{13}}{{15}} < \frac{7}{8} < \frac{8}{9}

8.  3 Girls and 4 boys are to be seated in a row on 7 chairs in such a way that all the three girls always sit together. In how many different ways can it be done ?

a

  720

b

  576

c

  144

d

  480

e

  None of these

Answer & Explanation
Answer : Option A
Explanation :

Total number of persons = 3 girls + 4 boys = 7

The girls always sit together. Considering three girls as one person, we have 5 persons who can be arranged in 5! ways. But corresponding to each way of these arrangements, the girls can be arranged together in 3! ways.

Hence, required number of ways

= 5! × 3! = 120 × 6 = 720

9.  In how many different ways can the letters of the word DRASTIC be arranged in such a way that the vowels always come together ?

a

  720

b

  360

c

  1440

d

  540

e

  None of these

Answer & Explanation
Answer : Option C
Explanation :

There are 7 letters in the word ’DRASTIC’ including 2 vowels (A,I) and 5 consonants (D,R,S,T,C,). Considering two vowels as one letter, we have 6 letters which can be ar - ranged in 6! ways. But corresponding to each way of these arrangements, the vowels can be put together in 2! ways.

Hence, required number of words = 6! × 2!

= 720 × 2 = 1440

10.  Area of circle is equal to the area of a rectangle having perimeter of 50cms. and length more than the breadth by 3 cms. What is the diameter of the circle?

a

  7 cms.

b

  21 cms.

c

  28 cms.

d

  14 cms.

e

  None of these

Answer & Explanation
Answer : Option D
Explanation :

Let the breadth of the rectangle be x cms.

\Rightarrow Length = (x + 3) cms.

Now, 2(x + x + 3) = 50

\Rightarrow 2x + 3 = 25

\Rightarrow 2x = 22

\Rightarrow x = 222=11\frac{{22}}{2} = 11

\therefore Breadth = 11cms. and length = x + 3 = 11 + 3 = 14 cms.

\therefore Area of circle = Area of rectangle

\Rightarrow π\pi r2 = 14 × 11

\Rightarrow r 2 = 14×11×722\frac{{14 \times 11 \times 7}}{{22}}

\Rightarrow r = 7 cms.

\therefore Diameter = 14 cms.

11.  38\frac{3}{8} of 47\frac{4}{7} of 79\frac{7}{9} of 738 = ?

a

  123

b

  132

c

  142

d

  143

e

  None of these

Answer & Explanation
Answer : Option A
Explanation :

?=38×47×79×738=123? = \frac{3}{8} \times \frac{4}{7} \times \frac{7}{9} \times 738 = 123

12.  325×417+123×215=  ?3\frac{2}{5} \times \frac{4}{{17}} + 1\frac{2}{3} \times \frac{2}{{15}} = \;?

a

  21452\frac{1}{{45}}

b

  11451\frac{1}{{45}}

c

  1191\frac{1}{9}

d

  1251\frac{2}{5}

e

  None of these

Answer & Explanation
Answer : Option B
Explanation :

?=175×417+53×215? = \frac{{17}}{5} \times \frac{4}{{17}} + \frac{5}{3} \times \frac{2}{{15}}

=45+29=36+1045 = \frac{4}{5} + \frac{2}{9} = \frac{{36 + 10}}{{45}}

=4645=1145 = \frac{{46}}{{45}} = 1\frac{1}{{45}}

13.  135% of 480 + ?% of 320 = 728

a

  25

b

  28

c

  125

d

  115

e

  None of these

Answer & Explanation
Answer : Option A
Explanation :

25

14.  36?=90195\frac{{36}}{?} = \frac{{90}}{{195}}

a

  76

b

  72

c

  78

d

  84

e

  None of these

Answer & Explanation
Answer : Option C
Explanation :

36?=90195\frac{{36}}{?} = \frac{{90}}{{195}}

90×?=36×195 \Rightarrow 90 \times ? = 36 \times 195

?=36×19590=78 \Rightarrow ? = \frac{{36 \times 195}}{{90}} = 78

15.  323.001 × 15 + ? = 5000.015

a

  145.014

b

  155

c

  145

d

  155.014

e

  None of these

Answer & Explanation
Answer : Option B
Explanation :

323.001 × 15 + ?

= 5000.015

4845.015 + 9 = 5000.015

? = 5000.015 – 4845.015

= 155

500
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