09-08 - 2015 ssc

Exclusively prepared by SSC Focus Team

Chennai: #1, South Usman Road, T Nagar. | Madurai: #24/21, Near Mapillai Vinayagar Theatre, Kalavasal. | Trichy: opp BSNL office, Juman Center, 43 Promenade Road, Cantonment. | Salem: #209, Sonia Plaza / Muthu Complex,

Junction Main Rd, State Bank Colony, Salem. | Coimbatore.

7601808080 / 9043303030 | www.RaceInstitute.in

an ISO 9001: 2008 Certified Institution

Is Now In CHENNAI | MADURAI | TRICHY | SALEM | COIMBATORE

www.RACEInstitute.in

51 Buffet SSC CGL

Advance Mathematics

Solved Paper Aug, 09 - 2015

R.A.C.E Rapid Academy of Competitive Exams

Chennai: #1, South Usman Road, T Nagar. Chennai. Mob: 9043303030 / 7601808080 Madurai: #24/21, Near Mapillai Vinayagar Theatre, Kalavasal. M: 7695814311 | www.RACEInstitute.in

2

09-08-2015 (1 Sitting):

1. In ABC, a line through A cuts the side BC

at D such that BD:DC = 4:5. If the area of

ABD = 60cm2, then the area of ADC is (in

cm2):

(a) 50 (b) 60

(c) 75 (d) 90

2. A tangent is drawn to a circle of radius

6cm from a point situated at a distance of

10cm from the centre of the circle. The

length of the tangent will be:

(a) 4 (b) 5

(c) 8 (d) 7

3. A ship after sailing 12 km towards south

from a particular place covered 5 km more

towards east. Then the straightway distance

of the ship from that place is:

(a) 18 (b) 15

(c) 13 (d) 11

4. Two poles of height 7m and 12m stand on

a plane ground. If the distance between

their feet is 12m, the distance between their

top will be:

(a) 13 (b) 19

(c) 17 (d) 15

5. The maximum value of value of

sin4 +cos4 is

(a) 1 (b) 2

(c) 3 (d)

6. Find the value of tan4° tan43° tan47°

tan86°

(a) 1 (b)

(c) 2 (d)

7. The sum of four numbers is 48. When 5

and 1 are added to the first two; and 3 & 7

are substracted from the 3rd & 4th the

numbers will be equal. The numbers are:

(a) 4,12,12,20 (b) 5,11,13,19

(c) 6,10,14,18 (d) 9,7,15,17

8. The least number that should be added to

2055, so that the sum is exactly divisible by

27:

(a) 24 (b) 27

(c) 31 (d) 28

9. A and B together can do a piece of work

in 6 days. If a can alone do the work in 18

days, then the number of days required for

B to finish the work is:

(a) 12 (b) 9

(c) 15 (d) 10

10. A pipe can fill a tank in x hours ad

another can empty it in y hours. They can

together fill it In (y>x):

(a) x-y (b) y-x

(c)

(d)

11. A tap cap empty a tank in 30mins A

second tap can empty it in 45mins. If both

the taps operate simultaneously, how much

time is needed to empty the tank?


Trichy: opp BSNL office, Juman Center, 43 Promenade Road, Cantonment. Mob: 9360703030 Salem: #209, Muthu Plaza, Junction Main Rd, State Bank Colony, Salem. Mob: 7305958080

3

3

(a) 18 mins (b) 14 mins

(c) 15 mins (d) 30 mins

12. The perimeter of one face of a cube is 20

cm. If volume will be:

(a) 100 cm3 (b) 125 cm3

(c) 400 cm3 (d) 625 cm3

13. If the area of a circle is A, radius of the

circle is radius circumference of it is C then.

(a) rC = 2A (b)

=

(c) AC =

(d)

= C

14. A square is inscribed in a quarter-circle

in such a manner that two of its adjacent

vertices lie on the two radii at an equal

distance from the centre, while the other

two vertices lie o the circular arc. If the

square has sides of length x, then the radius

of the circle is:

(a)

(b)

(c)

(d) x

15. 10% discount and then 20% discount I

succession is equivalent to total discount of:

(a) 15% (b) 30%

(c) 24% (d) 28%

16. The marked price of a watch was Rs

720. A man bought the same for Rs 550.80

after getting two successive discounts, the

first being 10%. The second discount rate is:

(a) 12% (b) 14%

(c) 15% (d) 18%

17. Allowing 20% and 15% successive

discounts, the selling price of an article

becomes Rs3060; then the marked price will

be:

(a) 4400 (b) 5000

(c) 4500 (d) 4000

18. Eighteen years ago, the ratio of A’s age

to B’s age was 8:13. Their present ratio’s

are 5:7. What is the present age of A?

(a) 70 (b) 50

(c) 40 (d) 60

19. 729 ml of a mixture contains milk and

water in the ratio 7:2. How much more

water is to be added to get a new mixture

containing mild and water in the ratio 7:3?

(a) 60 (b) 71

(c) 52 (d) 81

20. The average weight of 15 oarsman in a

boat is increased by 1.6 kg when one of the

crew, who weight 42Kg is replaced by a new

man. Find the weight of the new man (in

kg).

(a) 65 (b) 66

(c) 43 (d) 67

21. What is the arithmetic mean of the first

‘n’ natural numbers?

(a)

(b)

(c) 2(n+1) (d)

22. A shopkeeper bought 30 kg of rice at the

rate of Rs70 per kg and 20 kg of rice at the



4

rate of Rs70.75 per kg. If he mixed the two

brand of rice and sold the mixture at Rs

80.50 per Kg, his gain is:

(a) 510 (b) 525

(c) 485 (d) 450

23. The population of a town increase by 5%

every year. If the present population is

9261, the population 3 years ago was:

(a) 5700 (b) 6000

(c) 7500 (d) 8000

24. A farmer travelled a distance of 61 km in

9 hrs. He travelled partly on foot at the rate

of 4 km/hr and partly on bicycle at the rate

of 9 km/hr. The distance travelled on foot is:

(a) 17 (b) 16

(c) 15 (d) 14

25. Walking at the rate of 4 kmph a man

covers certain distance in 2 hrs 45 mins.

Running at a speed of 16.5 kmph the man

will cover the same distance in how many

mins?

(a) 35 mins (b) 40 mins

(c) 45 mins (d) 50 mins

26. In certain years a sum of money is

doubled itself at 6.25% simple interest per

annum, then therequired time will be:

(a) 12.5 years (b) 8 years

(c) 10.66 years (d) 16 years

27. The length of the portion of the straight

line 3x+4y=12 intercepted between the axes

is:

(a) 3 (b) 4

(c) 7 (d) 5

28. The value of:

–

+

-

+

is:

(a) 0 (b) 1

(c) 5 (d) 7

29. If m=-4, n=-2, then the value of m3-

3m2+3m+3n+3n2+n3 is

(a) 124 (b) -124

(b) 126 (d) -126

30. 2x-ky+7=0 and 6x-12y+15=0 has no

solution for:

(a) k=-4 (b) k=4

(c) k=1 (d) k=-1

31. Choose the incorrect relation(s) from the

following:

(1) 6+ 2 = 5+ 3

(2) 6+ 2 < 5+ 3

(3) 6+ > + 3

(a) 1 only (b) 2 only

(c) 1 and 3 (d) 2 and 3

32. If x = 332, y = 333, z = 335, then the

value of x3+y3+z3-3xyz is:

(a) 7000 (b) 8000

(c) 9000 (d) 10000

33. If

+

+

= 3, then the

value of m is

(a) + (b) + +

(c) - - (d)



5

5

35. The measure of an angle whose

supplement is three times as large as its

complement, is:

(a) 30° (b) 45°

(c) 60° (d) 75°

36. The sides of a triangle having area 7776

sq.cm are in the ratio 3:4:5. The perimeter

of the triangle is:

(a) 400cm (b) 412cm

(c) 424cm (d) 432cm

37. Two chords of length a unit and b unit of

a circle make angles 60° and 90° at the

centre of a circle respectively, and then the

correct relation is:

(a) b= a (b) b=2a

(c) b= a (d) b=1.5a

38. In a parallelogram PQRS, angle P is four

times of angle Q, then the measure of R is:

(a) 36° (b) 72°

(c) 130° (d) 144°

39. If sin +sin2 =1 then cos2 +cos4 is

equal to:

(a) 1 (b)

(c)

(d) none

40. If a clock started at noon, then the angle

turned by hour hand at 3.45PM is:

(a) 104.5° (b) 97.5°

(c) 112.5° (d) 117.5°

41. The numerical value of

+

-

-

is:

(a)

(b)

(c)

(d) 1

42. If xcos – sin = 1, then x2 + (1+x2)sin

equals:

(a) 1 (b) -1

(c) 0 (d) 2

43. A 10 m long ladder is placed against a

wall. It is inclined at an angle of 30 ° to the

ground. The distance (in m) of the foot of

the ladder fro the wall is (given =1.732)

(a) 7.32 (b) 8.26

(c) 8.66 (d) 8.16

Direction for the next four questions. The

number of the production of electronic items

(TVs and LCDs) in a factory during the

period from 2009 to 2013.



6

44. The total number of production of

electronic items is maximum in the year:

(a) 2009 (b) 2010

(c) 2011 (d) 2013

45. The ratio of production of LCDs in the

year 2011 and 2013 is:

(a) 3:4 (b) 4:3

(c) 2:3 (d) 1:4

46. The difference between average of

production of TVs and LCDs from 2009 to

2012 is:

(a) 600 (b) 700

(c) 800 (d) 900

47. The ratio of production of TVs in

theyears 2009 and 2010 is:

(a) 7:6 (b) 6:7

(c) 2:3 (d) 3:2

Direction for 48 to 50: The following pie

chart shows the sources of funds to be

collected by the National Highways Authority

of India (NHAI) for its phase II projects.

Study the piechart and answer the following

three questions:

48. If the toll is to be collected through an

outsourced agency by allowing a maximum

10% commission, how much amount should

be permitted to be collected by the

outsourced agency, so that the project is

supported with Rs 4910 crores?

(a) 6213 (b) 5827

(c) 5401 (d) 5316

49. If NHAI could receives a total of 9695

crores as external assistance, by what

percent (approx) should it increase the

market borrowing to arrange for the

shortage of funds?

(a) 4.5% (b) 7.5%

(c) 6% (d) 8%

50. The central angle corresponding to

market borrowing is:

(a) 52 (b) 137.8

(c) 187.2 (d) 192.4

Solution: 1.Solution: (c)

BD:DC=4:5

Area of ABD:Area of ADC=60:X

4/5= 60/X

X = 75 2.Solution: (c)

Tangent from a point to the circle will be perpendicular to the line drawn from the

centre to that point.



7

7

OP2=OA2+PA2

102=82+X2

100-64=X2

X=6

3. Solution: (c) In ABC,

122+52=X2

144+25=X2

169=X2

X=13 4. Solution: (a)

In ABC, AC2=AB2+BC2

122+52=X2

X=13

5. Solution: (a)

Put = 0

sin4 +cos4 = 0 + 1

= 1

So , the maximum value of expression is 1

6. Solution: (a)

Cot86 .cot47 .tan47 .tan86 =

.tan 47.tan 86 =1

7. Solution: (a) From the options: 6,10,14,18 6+5=11; 10+1 =11; 14-3=11 ; 18-

7=11 8. Solution: (a)

=

X=24 9.Solution: (a)

-

=

Hence in 9 days B can complete the work

10.Solution: (d)

-

=

Hence

11.Solution: (a)

+

=

Hence

= 18mins

12.Solution: (b) Perimeter of one face =4a=20

a=5

V =a3

=53=125cm3

13.Solution: (a) Area=A, radius=r,

Circumference=C

A= r2

A=

r.r

2A/r=C 2A=rC 14. Solution: (c)

R2=2x2+y2

2y2=x2

y2=x2/2 R2=2x2 + x2/2 R2=5x2/2

R=

x

15. Solution: (d) Let the amount be 100

10% discount is 90 20% discount of 90 is 18 Equivalent discount=100%-72%=28%

16. Solution: (c)

Let MP=720 10% discount=72



8

720-72=648

* 648 = 550.80

100 - x = 85 x=15%

17. Solution: (c)

x = 3060

X = 25 * 180 =4500

18. Solution: (b)

B=

13(A-18) = 8(

- 18)

65A - 1170 = 56A - 720

9A = 450 A = 50

19. Solution: (d)

Let the ratio of milk and

water are in the ratio of 7:2

*729=567

*729=162

=

1701=1134+7X

567=7X

Hence water to be added to the mixture is

X=81

20. Solution: (b)

Let the initial weight be 42. Weight

increased for 15 is 1.6kg when new one is

replacing the older one

42 + (1.6 * 15) =42 + 24 =66

21. Solution: (a)

Arithmetic mean of n natural numbers

= n(n+1)/2n

=(n+1)/2

22. Solution: (c)

Let the two variety of rice be 30kg and 20

kg of price Rs.70 and Rs.70.75 respectively.

Difference = S.P - C.P

50*80.50 - (30*70 + 20*70.75)

= 4025 - 3515

= 485

23. Solution: (d)

Let the principal be x, amount = 9261,r=5%

X (1+

)3 =9261

X (

)3 =213

X = 8000

24. Solution: (b)

From the option

x*4 + (9-x)*9 =61

Hence the distance travelled by foot is 16km

25. Solution: (b)

Distance travelled in 2hrs and 45 mins is

9km

Speed = distance / time

Running at the speed of 16.5km ,



9

9

time =

=

26. Solution: (d)

2x = x * n *

N =

N = 16

27. Solution: (d)

3x + 4y = 12

When, x = 0; y = 3

When, y = 0; x = 4

X and y intercepts are 4 & 3;

Z2 = x2 + y2

Z2 = 42 + 32

Z = 5

28. Solution: (c)

2 + 3 = 5

29. Solution: (d)

- 64 – 48 – 12 – 6 + 12 – 8 = - 126

30. Solution: (b)

For no solution; a = b

=

K = 4

31. Solution: (b)

3.86 < 3.968

32. Solution: (d)

X3 + y3 + z3 – 3xyz

=

(x + y + z)

[(x – y)2 + (y – z)2 + (z – x)2]

= 500 * 14

= 7000

33. Solution: (b)

+

+

=3

-1+

-1 +

-1=0

+

+

=0

m-a2-b2-c2+ m-a2-b2-c2+ m-a2-b2-c2 =0

m = a2 + b2 + c2

35. Solution: (b)

3 ( 90 - x ) = 180 – x

270 – 3x = 180 –x

90 = 2x

45 = x

36. Solution: (d)



10

Let the ratio off sides o the triangles be 3x :

4x : 5x

Area of the triangle = ½* 3x*4x = 7776

X2 = 1296

X = 36

Perimeter = (3 + 4 +5)x = 12 * 36 = 432

37.Solution; (a)

All the angles are equal in a equilateral

triangle(60) whereas 2 angles are equal in

isosceles triangle

Sin 45 =

=

=> b=

38. Solution: (d)

Sum of all the angles = 360

Opposite angles are equal in a parallelogram

X + 4x + x + 4x = 360

10x = 360

X =36

Angle R = 4x = 4* 36 = 144

39.Solution: (a)

Sin a = 1 – sin 2 a = cos2 a

To find cos2 a + cos4 a= cos2 a + sin2

a =1

40. Solution: (c)

Let the total angle be 360.

Angle made by the hour hand from

noon is = 3*30 + 30 *3/4

=90 + 22.5

= 112.5

41. Solution: (a)

Given eqn =

+

-

-

=

-

-

+

=

=

=

42. Solution: (a)

Let us take =0 and x=1

Hence x2+ (1 + x2) sin = 1 + 0 =1

43. Solution: (c)

Cos 30 =

=

X = 8.66

44. Solution: (c)

Total no. of production is maximum in the

year 2011

22,000

45. Solution: (a)

Ratio of LCD in 2011 : 2013 = 9000 : 12000

= 3 : 4

46. Solution: (d)

Diff b/w the average of production of TVs

and LCDs is

=

= 900

47. Solution: (c)



11

11

Ratio of production of TVs in the year 2009

and 2010 is

2009 : 2010 = 6000 : 9000 = 2:3

48. Solution: (c)

Max amount permitted to collect from toll is

= 4910 + 4910*10/100

=4910+491 = 5401

49. Solution: (c)

Loss in external assistance = 11,486 – 9695

= 1791

% rise in market borrowing =

* 100

= 6( approx)

50. Solution: (c)Central angle corresponds to

market borrowing is

09-08-15 (2nd sitting):

1. Find the square root of:

(a)

(b)

(c) 3 (d)

2. IF the cube root of 79507 is 43, then the

value of:

is:

(a) 4.773 (b) 47.73

(c) 0.4773 (d) 477.3

3. A can do a work in 10 days and B in 20

days. If they together work on it for 5 days,

then the fraction of the work that is left is:

(a)

(b)

(c)

(d)

4. Pipe A can fill a tank in 4 hours and pipe B

can fill it in 6 hours. If they are opened on

alternate hours and if pipe A is opened first

then in how many hours, the tank shall be

full?

(a) 4

(b) 4

(c) 3

(d) 3

5. A,B and C can do a piece of work in 24,

30 and 40 days respectively. They began the

work together but C left 4 days before

completion of the work. In how many days

was the work done?

(a) 11 (b) 12



12

(c) 13 (d) 14

6. The length of canvas 75cm wide required

to build a conical tent of height 14 m and the

floor area of 346.5m2 is:

(a) 665m (b) 770m

(c) 490m (d) 860m

7. The percentage increase in the surface

area of a cube when each side is doubled is:

(a) 200% (b) 300%

(c) 150% (d) 50%

8. The ratio of each interior angle angle to

each exterior angle of a regular polygon is

3:1. The number of sides of the polygon is:

(a) 6 (b) 7

(c) 8 (d) 9

9. List price of a book is Rs 100. A dealer

sells three such books for Rs 274.50 after

allowing discount at a certain rate. Find the

rate of discount.

(a) 8.33% (b) 8.16%

(c) 8.5% (d) 8.34%

10. The printed price of an article is 40%

higher then its cost price. Then the rate of

discount so that he gains 12% profit is:

(a) 20% (b) 15%

(c) 21% (d) 18%

11. A shopkeeper gains 17% after allowing a

discount of 10% on the Marked price of an

article. Find his profit percent if the article is

sold at marked price allowing no discount.

(a) 23% (b) 27%

(c) 30% (d) 37%

12. The measures of two angles of a triangle

is in the ratio 4:5. If the sum of these two

measures is equal to the measure of the

third angle. Find the smallest angle.

(a) 90 (b) 50

(c) 10 (d) 40

13. A and B entered into a partnership

investing Rs 16000 and Rs 12000

respectively. After 3 months A withdrew Rs

5000 while B invested Rs %5000 more. After

3 more months C joins the business with a

capital of Rs 21000. The share of B exceeds

that of C out of a tatal profit of Rs 26400

after 1 year by.

(a) 1200 (b) 2400

(c) 4800 (d) 3600

14. Out of four numbers the average of the

first three is 16 and that of the last three is

15. If thelast number is 20 then the number

is:

(a) 25 (b) 21

(c) 23 (d) 28

15. The average of 7,11,15,x,14,21,25 is 15,

then the value of x is:

(a) 3 (b) 14.5

(c) 12 (d) 13.3

16. Cost price of 100 books is equal to the

selling price of 60 books. The gain

percentage or loss percentage is:



13

13

(a) 66% (b) 66

(c) 66

% (d) 67%

17. A man spends 75% of his income. His

income is increased by 20% and he

increased his expenditure by 10%. His

savings are increase by:

(a) 10% (b) 25%

(c) 37

% (d) 50%

18. Raj and Prem walk in opposite direction

at the rate of 3 km and 2 km per hour

recpectively. How far will they be from each

other after 2 hrs?

(a) 8km (b) 10km

(c) 2km (d) 6km

19. A boat can travel with a speed of 13

km/hr in still water. If the speed of the

stream is 4 km/hr in the same direction,

time taken by boat to go 63km in opposite

direction is:

(a) 7 (b) 9

(c) 3

(d) 4

20. A sum of money lent out at simple

interest amounts to Rs 720 after 2 years and

Rs 1020 after a further period of 5 year. Find

the principle.

(a) 6000 (b) 600

(c) 1740 (d) 120

21. If m-5n = 2, then the value of (m3 –

125n3 – 30mn) is:

(a) 6 (b) 7

(c) 8 (d) 9

22. Given that x3 + y3 = 72 and xy = 8 with

x>y, then the value of x-y is:

(a) 4 (b) 2

(c) 02 (d) -4

23. If x =

, then the value

of x is:

(a) (b)

(c) (d)

24. If x+

= 2, then the value of –

is:

(a) -4 (b) 4

(c) 2 (d) 0

25. If

=

, the ratio of (2x + 3y) and (3y –

2x) is:

(a) 2:1 (b) 3:2

(c) 3:1 (d) 1:1

26. If x +

= 1 , then the value of

is:

(a)

(b)

(c) 2 (d) 1

27. A number exceeds its two fifth by 75.

The number is:

(a) 125 (b) 100

(c) 112 (d) 150

28. If the sum of two numbers, one of which

is

times the other is 50, then the numbers

are:

(a)

,

(b)

,



14

(c)

,

(d)

,

29. Two circles touch externally. The sum of

their areas is 130 sqcm and the distance

between their centres is 14 cm. the radius of

the smaller circle is:

(a) 2 (b) 3

(c) 4 (d) 5

30. ABC is a triangle and the sides AB, BC

and CA are produced to E,F and G

respectively. If CBE = ACF = 130 , then

the value of GAB is:

(a) 100 (b) 80

(c) 130 (d) 90

31. If two medians BE and CF of a triangle

ABC, intersects each other at G and if BG =

CG, BGC = 60 , BC = 8 cm, then area of

the triangle ABC is:

(a) 96 cm2 (b) 48 cm2

(c) 48cm2 (d) 64 cm2

32. In a rhombus ABCD, A = 60 , and AB =

12cm. then the diagonal BD is:

(a) 2 cm (b) 6cm

(c) 12cm (d) 10cm

33. If two supplementary angles differ by

44 , then one of the angles is:

(a) 102 (b) 65

(c) 68 (d) 72

34. If PQRS is a rhombus and SPQ = 50 ,

then RSQ is:

(a) 75 (b) 45

(c) 55 (d) 65

35. ABC is a cyclic triangle and the bisectors

of BAC, ABC and BCA meet the circle at

P, Q and R respectively. Then the angle

RQP is:

(a) 90 -

(b) 90 +

(c) 90 -

(d) 90 +

36. XY and XZ are tangents to a circle. ST is

another tangent to the circle at the point R

on the circle, intersects XY and XZ at S and

T respectively. If XY = 15cm and TX = 9cm,

then RT is:

(a) 4.5cm (b) 3cm

(c) 7.5cm (d) 6cm

37. The simplified form of the given

expresition sinAcosA(tanA-cotA) is (where

0 ):

(a) 1 (b) 1- cos2A

(c) 1-2sin2A (d) 2sin2A-1

38. If

= n and

= m, then the value of

cos2 is:

(a)

(b)

(c) 0 (d)

39. The value of

tan1

(a) 1 (b) 0

(c) -1 (d) none

40. If tan + cot =5, then tan2 +cot2 is:

(a) 23 (b) 24



15

15

(c) 25 (d) 26

41. The angle of elevation of a tower from a

distance 100mtr. From its foot is 30 . Then

the height of the tower is:

(a)

(b) 100

(c)

(d) 50

42. A person of height 6ft. wants to pluck a

fruit which is on a

ft. high tree. If the

person is standing

ft. away from the base

of the tree, then at what angle should he

through a stone so that, it hits the fruit?

(a) 30 (b) 45

(c) 60 (d) 75

43. If is an acute and tan2 +

= 2,

then the value of is:

(a) 45 (b) 30

(c) 60 (d) 15

Direction for 44 to 47:

The graph shows the demand and production

of different companies.Y axis represents the

unit in lakh metric tons. X axis represents

the companies.

44. What is the ratio of the companies

having more demand than production to

those having more production than demand?

(a) 1:2 (b) 2:3

(c) 2:1 (d) 3:2

45. What is the difference between the

average demand and the average production

of the companies (in lakh tones)?(approx)

(a) 200 (b) 250

(c) 275 (d) 325

46. The demand of company B is what

percentage of the production of company F?

(a) 50% (b) 70%

(c) 55% (d) 65%

47. The production of company A is

approximately what percent of the demand

of company C?

(a) 50% (b) 60%

(c) 55% (d) 65%

Direction for 48 to 50: Given a line graph

showing the number of students passed in

higher secondary examination in a school

over the years from 2008 to 2013:

1450

3660 3100

4200 3700

4500

2100

3150 2600

5000

2800 3300

0

1000

2000

3000

4000

5000

6000

A B C D E F

Production Demand

110

138 145

170

156 160

0

20

40

60

80

100

120

140

160

180

2008 2009 2010 2011 2012 2013



16

48. The average of passed students in the

years 2008, 2009, 2012 approximately is:

(a) 134.56 (b) 134.67

(c) 134.41 (d) 134.32

49. The decrease in percentage of students

from 2011 to 2012 approximately:

(a) 8.22% (b) 8.27%

(c) 8.25% (d) 8.24%

50. The increase in percentage of passed

students from 2008 to 2011 approximately

is:

(a) 55% (b) 54.5%

(C) 50.5% (d) 53.05%

Solution:

1.

=

2.

=4.3+0.043+0.043

=4.773

3.work done in 5 days=

+

=

+

=

Work left is = 1-

=

4.pipe A and B together can fill the tank in 2

hours ;

=

+

=

Tank fill in 4 hours =

=

Remaining tank = 1-

=

Remaining tank filled by pipe A in = 4*

=

Tank fill in 4

hours.

5. If work was done in “X” days

+

+

= 1

= 1

12x-12=120

12x=132

X=11 days

6. radius of conical tent = r m

=346.5

=

*7

r=10.5m

= +

= +

L = 17.5



17

17

Length of canvas =

=

= 770m

7. Side of the cube = a

Surface area =

Side of the new cube = 2a

Surface area of new cube = 6*(2 ) = 24

Percentage increase =

* 100

=

* 100

= 300%

8. Number of sides = n

= 3

= 3

n-2 = 6

n=8

9. rate of discount is “x”

300(

) = 274.5

100-x = 91.5

X = 100 – 91.5

X = 8.5%

10. rate of discount = r%

40=

200-2r = 60 + 5r

7r = 140

R= 20%

11. marked price = “x”

c.p =

s.p = x

profit percent =

=

=30%

12.

4x , 5x, Y

4x+5x=Y

Y=9x

4x+5x+9x=180

X=10

Smallest angle = 10*4 = 40

13.

A:B:C=(16000*3+11000*9):(12000*3+17000*9):(21000

*6)

= 147000: 189000: 126000

= 7:9:6

Share of B =

*26400

=10800

Share of C =

*26400 = 7200

B exceeds that of C = 10800 – 7200 = 3600

14. sum of first three numbers = 16*3 = 48

Sum of last three numbers = 15*3 =45

First number = 20 = 48-45

First number = 3+ 20 = 23



18

15.

= 15

93 + x =105

X=12

16.gain percentage =

* 100

=

*100

=66

17. Consider income = 100

Expenditure =

= 75

Saving = 100 -75 = 25

New income =

= 120

New expenditure =

= 82.5

New saving = 120 – 82.5 = 37.5

Saving are increased by =

* 100

= 50%

18. required distance = (3*2)+(2*2)= 10 km

19. u=13km/hr

V=4km/hr

Required time =

=

=7hrs

20. suppose the principal is rs.P.

Then, p+

=720----------(1)

P+

= 1020-------(2)

On solving 1 and 2,

= 300

=60

Therefore, P+2*60 = 720

P=600

21. if m-5n=2

Then, -125 - 30mn

= - ( ) – 3*m*5n(m-5n)

=(m-5n)^3

= = 8

22. x = 2

23. x =

=a

= (a

= bx

x =

24. x+

=2

+1 = 2x

=0

X=1

Now, -

=1-1=0

Hence the smallest angle = 4*10=40

25.

=

=

=

=3:1



19

19

26. x+

=1

+1=x

Now,

=

=

=

27. suppose the number is “x”.

Then, x-

=75

=75

X=

=125

28. suppose numbers are “x” and

Then, x+

=50

=50

X=

Now, the numbers are

,

29. suppose radius of the circles are r1 and r2.

Then, r1 + r2 = 14--------1

π + = 130

+ =130--------2

On solving 1 and 2,

=3cm, =11cm

30.

Angle GAB = x0

Then, x+130+130=360

X+260=360

X=

31.

Area of ∆BCG=

*

=16

Now, area of ∆ABC = *area of ∆BCG

=3*16

= 48

32. In OAB, =

=

OB=6cm

Now, the diagonal BD=2*OB

=2*6=12cm 33. X+Y= --------1 X-Y= ----------2 On solving 1 and 2, X= , Y= 34. = - = - =

Now, =

=

=

35. = -

36. XZ=XY=15cm TZ=XZ-TX TZ=15-9 =6cm Now, RT = TZ = 6cm



20

37. (

=

–

=

)

= = -(1-

=2

38.

=m

=

=

=

=

( =

=

39. 1

40. tan + cot = 5

Squaring on both sides we get,

(tan + cot =(5

=25-2

=23

upp e he he gh f he wer “h”

Then, tan 3 =

=

h=

m.

42. Suppose angle is “ ”.

Then, in ∆ADE,

AE=BC=

ft

DE=

-6 =

Now, tan =

tan =

*

=3

43. +

=2

+1=2

( =0

=1=tan 4

=4

44. Required ratio= 2:4=1:2

45. Average demand,

=

=3158.33 lakh

Average production,

=

= 3435 lakh

Required difference = 3435- 3158.33

= 275

46. Required percentage =

=70%

47. Required percentage =

=55%

48. The required average of passed students,

=

=134.67

49. The decrease in percentage=

*100

= 8.24%

50. The increase in percentage=

*100

=54.5%

09-08 - 2015 ssc

Documents

Transcript of 09-08 - 2015 ssc