ACE OF PACE (MAIN) CODE 11
ACE OF PACE OBJECTIVE SECTION
1.
Sol.
2.
Sol.
3.
A contractor employs 200 men to build a bund. They finish 5/6 of the work in 10 weeks. Then rain
sets in and not only does the work remain suspended for 4 weeks but also half of the work already
done is washed away. After the rain, when the work is resumed, only 140 men turn up. The total time
in which the contractor is able to complete the work assuming that there are no further disruptions in
the schedule is :
(A) 25 weeks
(B) 26 weeks
(C) 24 weeks
(D) None of these
(C)
Laxman travels a certain distance by a car at the rate of 12 km/h and walks back at the rate of 3
km/h. The whole journey took 5 hours. What is the distance he covered on the car?
(A) 12 km
(B) 30 km
(C) 15 km
(D) 6 km
(A)
Amit has a cylindrical candle mold with the dimensions shown in fig.. If he has a rectangular block
of wax that measures 12 cm by 10 cm by 20 cm, about how many candle can he make after melting
the block of wax?
2.2 cm
5.0 cm
Sol.
4.
Sol.
5.
Sol.
6.
(A) 31
(A)
(B) 35
(C) 69
(D) 76
A father said to his son, “I was as old as you are at the present at the time of your birth”. If the
father’s age is 48 years now, the son’s age five years back was :
(A) 14 years
(B) 19 years
(C) 33 years
(D) 38 years
(B)
A train leaves Pune at 7.30 a.m. and reaches Mumbai at 11.30 a.m. Another train leaves Mumbai at
9.30 a.m. and reaches Pune at 1 p.m. At what time the two trains cross each other?
(A) 10.20 a.m.
(B) 10.26 a.m.
(C) 10.32 a.m.
(D) 11 a.m.
(B)
Sol.
The average weight of 29 students is 40 kg. If the weight of their teacher be included the average
weight is increased by 300 gms. The weight of the teacher is
(A) 49 kg
(B) 48.7 kg
(C) 49.3 kg
(D) none of these
(A)
7.
How many squares are there in the following figures?
(A) 10
(B) 11
(C) 12
(D) 13
Sol. (B)
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8.
In the given figure, ABC is right-angled at B such that BC = 6 cm and AB = 8 cm. A circle with
centre O has been inscribed inside the triangle. OP AB, OQ BC and OR AC.
If OP = OQ = OR = x cm, then x = ?
8 cm
A
P
B
x
x
R
O
x
Q
C
6 cm
Sol.
9.
Sol.
10.
Sol.
11.
Sol.
12.
(A) 2 cm
(A)
(B) 3 cm
(C) 2.5 cm
(D) 4 cm
Narayan Murthy walking at a speed of 20 km/h reaches his college 10 minutes late. Next time he
increases his speed by 5 km/h, but finds that he is still late by 4 minutes. What is the distance of his
college from his house?
(A) 20 km
(B) 12 km
(C) 10 km
(D) 30 km
(C)
When x3 – 6x2 + 12x – 4 is divided by x – 2, the remainder is
(A) 0
(B) 4
(C) 5
(B)
(D) 6
In a circle of radius 10 cm, a chord is drawn 6 cm from its centre. If an another chord, half the length
of the original chord were drawn, its distance in centimeters from the centre would be :
(A) 84
(B) 9
(C) 8
(D) 3
(A)
PQRS is a diameter of a circle whose radius is r. The lengths of PQ, QR and RS are equal. Semicircles are drawn on PQ and QS to create the shaded figure below : The perimeter of the shaded
figure is :
P
(A) r  2r
(B)
4 r
3
Q
R
(C)
S
5r
3
(D)
3r
2
Sol.
(A)
13.
In a class of 100 students there are 70 boys whose average marks in a subject are 75. If the average
marks of the complete class are 72, then the average marks of the girls
(A) 73
(B) 65
(C) 68
(D) 74
(B)
Sol.
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1

x3
(B) 198
14.
If x  3  8 then x 3 
Sol.
(A) 216
(B)
15.
Sol.
16.
Sol.
17.
Sol.
If x  1  1  1  1  ...... , then :
(A) x = 1
(B) 0 < x < 1
(C)
(C) 192
(D) 261
(C) 1 < x < 2
(D) x is infinite
Consider the following statements
1.
x – 2 is a factor of x 3  3x 2  4x  4
2.
x + 1 is a factor of 2x3  4x  6
3.
x – 1 is a factor of x 5  x 4  x 3  x 2  x  1 .
Of these statements
(A) 1 and 2 are correct
(B) 1, 2 and 3 are correct
(C) 2 and 3 are correct
(D) 1 and 3 are correct
(A)
In a school, 30 boys and 20 girls entered the IIT-JEE competition. Certificates were awarded to 10%
of the boys and 20% of the girls. Of the students who participated, the percentage that received
certificates was
(A) 14
(B) 15
(C) 16
(D) 30
(A)
If 30 boys entered the Exam and 10% of them received certificates, this implies that (0.1)(30 or 3 boys
received certificates. Of the 20 girls who entered the competition (0.2)(20) or 4 girls received certificates. This
implies that 7 students in total out of 50 received certificates. Thus 14% of the students in total received
certificates.
18.
Sol.
If a clock shows 12: 24 then its mirror image will be ?
(A) 11 : 46
(B) 11:36
(C) 91:36
(B)
19.
In the diagram, ABCD is a rectangle with AD 13, DE 5 and EA= 12. The area of ABCD is
Sol.
(A) 39
(B)
(B) 60
(C) 52
(D) 21:46
(D) 30
Since 132 = 122 + 52 we use the converse of Pythagorus’ Theorem to conclude that ∠AED=90°.
1
The area of Δ AED is then  5 12   30. Through E, we draw a line parallel to CD and BA. Since the area of
2
Δ FDE equals the area of ΔCDE we label each of these areas A. Similarly, the area of Δ AFE equals the area
of
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Δ BAE and so each of these areas can be labelled B. Since A +B = 30 , the area of the rectangle is 2(A + B) or
2(30) = 60.
20.
Sol.
A sealed bottle, which contains water, has been constructed by attaching a cylinder of radius 1 cm to
a cylinder of radius 3 cm, as shown in Figure A. When the bottle is right side up, the height of the
water inside is 20 cm, as shown in the cross-section of the bottle in Figure B. When the bottle is
upside down, the height of the liquid is 28 cm, as shown in Figure C. What is the total height, in cm,
of the bottle?
(A) 29
(A)
(B) 30
(C) 31
(D) 32
We’ll start by representing the height of the large cylinder as h1 and the height of the small cylinder as h2. For
simplicity, we’ll let x = h1 + h2.]
If the bottom cylinder is completely filled and the top cylinder is only partially filled the top cylinder will have
a cylindrical space that is not filled. This cylindrical space will have a height equal to x – 20 and a volume
equal to, (1)2 (x – 20).
Similarly, if we turn the cylinder upside down there will be a cylindrical space unfilled that will have a height
equal to x – 28 and a volume equal to, (3)2(x – 28).
Since these two unoccupied spaces must be equal, we then have,
(1)2(x – 20) = (3)2(x – 28)
x – 20 = 9x – 252
8x = 232
x = 29
Therefore, the total height is 29.
21.
Sol.
The circle with centre A has radius 3 and is tangent to both the positive x-axis and positive y-axis, as
shown. Also, the circle with centre B has radius 1 and is tangent to both the positive x-axis and the
circle with centre A. The line L is tangent to both circles. The y-intercept of line L is
(A) 9  3 3
(A)
(B) 10  3 2
(C) 8 3
(D) 10  2 3
We start by drawing a line from point C that will pass through A and B. From A and B, we drop perpendiculars
to the points of tangency on the x-axis and label these points as E and F as shown. We also drop a
perpendicular from A to the y-axis which makes AH = AE = 3.
Extracting CAE from the diagram and labelling with the given information we would have
the following noted in the diagram.
If we represent the distance from C to B as x and recognize that CBF is similar to CAE,
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x x4

1
3
x = 2.
FC2 = 22 – 12 = 3
In CBF,
FC =
3, (FC > 0).
This implies that BCF = 30 and OCD = 60. Therefore EF = . 2 3, from
similar triangles again.
This now gives us the diagram shown.
Thus, d  3 3  3 3  3 3  9

22.
Sol.
23.
Sol.
24.
Sol.
25.
Sol.

A man shows his friend a woman sitting in a park and says that she is the daughter of my
grandmother's only son. What is the relation between the two?
(A) Brother-Sister
(B) Husband-Wife
(C) Mother-Son
(D) None of these
(A)
A monkey starts climbing up a tree 20ft. tall. Each hour, it hops 3ft. and slips back 2ft. How much
time would it take the monkey to reach the top?
(A) 18
(B) 19
(C) 20
(D) 21
(A)
First day of year 1999 is Sunday, then what day is the last day of year 1999?
(A) Sunday
(B) Monday
(C) Tuesday
(D) Saturday
(A)
A man earns Rs. 20 on the first day and spends Rs. 15 on the next day. He again earns Rs. 20 on the
third day and spends Rs. 15 on the fourth day. If he continues to save like this, how soon will he have
Rs. 60 in hand?
(A) on 17th day
(B) on 27th day
(C) on 30th day
(D) on 40th day
(A)
Sol.
x
1 x 2
4  8 
If   .  
 , then x equals
3
 9   27 
(A) 1
(B) 2
(B)
27.
36 9
Simplify
a
Sol.
(A) a16
(B) a12
(D)
916 13 4 913 16 4
a    .a     a 2 .a 2  a 4
26.
28.
Sol.
4
63 9
a
(C) 3
(D) 4
(C) a8
(D) a 4
4
; the result is:
Which of the following fractions is less than 1/3
(A) 22/62
(B) 15/46
(C) 2/3
(B)
(D) 1
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29.
Sol.
30.
x 3
xy
is
 , then
y 2
xy
4
1
(A)
(B)
3
2
(D)
If
(C)
5
4
(D) 5
Sol.
A boy walks from home at 4 km/hr and reaches school 5 mins late. The next day, he increases his
1
speed by 1 km/hr and reaches 2 minutes early. How far is the school from his home?
2
1
1
(A) 3 km
(B) 3 km
(C) 2 km
(D) 2 km
2
2
(C)
31.
Simplify:
Sol.
(A) 1
(B)
2
1
3


5 3
3 2
5 2
(B) 0
(C) 10
Sol.
1
1
1
1
1





3 8
8 7
7 6
6 5
52
(A) 0
(B) 1
(C) 3
(D)
33.
If
Sol.
(A) 32
(D)
32.
34.
Sol.
(D) 100
(D) 5
2 2 2 2 2 = x, then x =
(B) 232
1
31
(C) 2 32
(D) 2 32
If you were to assemble these pieces into a circle, what would the figure formed by the inner lines
look like? (Assume all pieces are identical and they form a circle perfectly).
(A) Circle
(D)
(B) square
(C) hexagon
(D) pentagon
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35.
Area of shaded portion as shown in the given figure is
F
E
4m
2m
G
D`
C
A
1m
B
3m
Sol.
36.
(A) 5 m2
(B) 6 m2
(C) 7 m2
(B)
Area of shaded portion
= Area of rect. ABCG + Area of rect. GDEF
= (3 × 1) + (3 – 2) (4 – 1)
= 3 + 1 × 3 = 3 + 3 = 6 m2
(D) 8 m2
The diagram shows six equal circles inscribed in equilateral triangle ABC. The circles touch
externally among themselves and also touch the sides of the triangle. If the radius of each circle is R,
area of the triangle is
A
C
B


(A) 6   3 R 2
Sol.

(B) 9 R 2
(C) R 2 12  7 3

(D)none of these
(C)
3 2
a
4
R
x
 3R
tan 30
a  4R  2x  4  2 3 R


A

2
3
4  2 3 K2
4
 3 4  3  4 3 R2







 12  7 3 R 2
37.
B
C
25 men can do a project in 20 days. 15 men leave the project after working for some time, and the
1
remaining project is completed in next 37 days. After how many days did those 15 men leave?
2
(A)5 days
(B)7 days
(C)10 days
(D)none of these
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Sol.
(A)
After x days, 15 men leave the project.
1
In one day, one man does
job.
20  25

For x days working, 25 men do
x  25
job.
20  25
1
1
2 job.
In 37 days, 10 men do
2
20  25
x
375

1

20 20  25

25x + 375 = 500

x = 5.
10  37
38.
Sol.
If the price of gold increases by 30%, by what percent quantity of gold ornaments should be reduced
so that the expenditure remains the same as before?
1
1
(A) 23 %
(B) 27 %
(C)30%
(D)none of these
13
13
(A)
Let x be the quantity (in gm, say) purchased at old rate and y be the quantity purchased
at new rate.
100 x = 130 y
Reduction =
39.
Sol.
40.
Sol.
41.
a:b=3:
(A)5 : 12
(A)
a b c
  
b c d

y
100x
30
x 
x
130
130
30
1
100  23 %
130
13
4 , b : c = 7 : 9 , c : d = 5 : 7 , then a : d is
(B)7 : 12
(C)3 : 11
(D)none of these
3 7 5 5 a
   
4 9 7 12 d
A jar contains 10 red and 30 green marbles. How many more red marbles to be added to the jar so
that 60% of the marbles will be red?
(A)35
(B)45
(C)75
(D)none of these
(A)
10  x 3

40  x 5
Let x make red marbles be added
x  10
100  60
x  40
 5x + 50 = 3x + 120
 x = 35
A factory is open for exactly 20 days each month and produces 80 machinery parts each day, it is
open. How many years will it take to produce 96,000 parts?
(A) less than 5
(B)5
(C) more than 5 but less than 10
(D) more than 10
Sol. (B)
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In 20 days, 1600 parts are produced.

In a month, 1600 parts are produced (as the factory is open for 20 days
only).
To produce 96,000 parts 60 months are required.
42.
Sol.
43.
Sol.
If x varies inversely wit h y and varies directly wit h z. If y and z both are 12 when x = 3,
what is the value of y + z when x = 4?
(A) 9
(B)16
(C)25
(D) none of these
(C)
xy = k, x = 3, y =12 k = 36.
xy = 36
x
Also
= c ,x = 3, z = 12
z
1

c =
4

z = 4x.
36

y
9 
when x = 4
x
  y + z = 25
z  4x  16
If x 2  x  42   x  k  x  6  then the value of k is,
(A) 6
(B)  6
(C) 7
(D)
(D)  7
x2  x  42  x2  7 x  6x  42
 x  x  7  6 x  7
  x  6  x  7 
44.
Sol.
45.
Sol.
A three digit number ‘XYZ’ is such that Y + Z is divisible by 3. For what value of X, X + Y + Z will
be divisible by 3 ?
(A) 1
(B) 2
(C) 3
(D) 4
(C)
Y+Z is divisible by 3. So for XYZ to be divisible by 3 X+Y+Z should be divisible by 3, which
would leave only one option.

= 84 – 7 [–3x + 12]
46.
Sol.


The value of 84  7 11x  4 17 x  3 8  9  5 x 


(A) 21x
(B) 21 x
(C) 45 x
(D) 45
(A)
LHS = 84 – 7 [–11x – 4 {–17x+3(8 – 9 + 5x)}]
= 84 – 7 [– 11x – 4 {– 17x – 3 + 15x}]
= 84 – 7 [– 11x – 4 {– 2x – 3}]
= 84 – 7 [–11x + 8x + 12]
 84  21x  84  21x
If 7 spiders make 7 webs in 7 days, then 1 spider will make 1 web in how many days?
7
(A) 1
(B)
(C) 7
(D) 49
2
(C)
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Let the required number of days be x . Then,
Less spiders, More days
(Indirect Proportion)
Less webs, Less days
(Direct Proportion)
Spiders 1: 7 

 ::7 : x
Webs 7 :1 
 1 7  x  7 1 7  x  7
47.
In the given figure, AB & AC are 2 tangents to the circle, whose centre is O . If BAC  50 ,
then  BDC is
B
o
A
D
C
Sol.
(A) 65
(A)
(B) 60
BOC  180  50  130
48.
Sol.
(C) 75
BDC 
;
(D) 70
130
 65o
2
A and B can together finish a work in 30 days. They worked together for 20 days and then B left.
After another 20 days, A finished the remaining work. In how many days A alone can finish the job?
(A) 40
(B) 50
(C) 54
(D) 60
(D)
 A  B  ' s 20 day’s work
 1
 2
 2 1
   20   . Remaining work  1   
 30
 3
 3 3
1
work is done by A in 20 days.
3
Whole work will be done by A in  20  3   60 days.
Now,
49.
Sol.
The average weight of 45 students in a class is 52 kg. Five of them whose average weight is 48 kg
leave the class and other 5 students whose average weight is 54 kg join the class. What is the new
average weight (in kg) of the class?
1
1
2
(A) 52
(B) 52
(C) 52
(D) None of these
3
2
3
(C)
Sum of the weights of the students after replacement
  52  45    48  5    54  5   kg  2370 kg
2370
2

New average  
 kg  52 kg .
3
 45 
50.
Today is Wednesday. What day of the week will it be 100 days from now?
(A) Monday
(B) Tuesday
(C) Thursday
(D) Friday
Sol.
(D)
Since there are 7 days in a week it will be Wednesday in 98 days. In 100 days it will be Friday
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