### Find solutions for all the questions at the end of each set:

### Set A

1. A bag contains some Rs. 5 Coins. Rs. 2 coins and Rs. 1 coins with total number of coins being 52, and the total amount being Rs. 125. The number of five rupee and two rupee coins is 37. The numbers of Rs. 5 coins are ………

(a) 12

(b) 15

(c) 18

(d) 21

2.The sum of the ages of A and B is four-third the age of C. The age of B is two-thirds the age of C. If the sum of the ages of the three persons is 35 years, find the age of B.

(a) 20 years

(b) 10 years

(c) 18 years

(d) 15 years

3. There are four numbers P, Q, R andS. P is 1/3rd is of the total of Q, R and S. Q is 1/4th of the total of the P, R and S. R is 1/5th of the total of P, Q and S. If the total of the four numbers is 3480, then find the value of S.

(a) 1240

(b) 1334

(c) 1567

(d) Cannot be determined

4. Ajay and Vijay have some marbles with them. Ajay told Vijay “if you give me x marbles, both of us will have equal number of marbles”. Vijay then told Ajay “if you give me twice as many marbles, I will have 30 more marbles than you would”. Find x.

(a) 4

(b) 5

(c) 6

(d) 8

5. A man travelled a total distance of 1800 km by plane, train and bus. He travelled one –third of the whole trip by plane and the distance travelled by train is three-fifth of the distance travelled by bus. Find the distance travelled by bus.

(a) 450 km

(b) 850 km

(c) 1200 km

(d) 750 km

6. Ajay bought a total of 12 oranges and 18 bananas for Rs. 84. When the cost of each orange doubles, he could buy 6 oranges and 16 bananas for Rs. 80. Find the cost of each banana.

(a) Rs. 3

(b) Rs. 2

(c) Rs. 4

(d) Rs. 5

7. The cost of one pen and two books together is Rs. 70. The cost of three pens and nine books together is Rs. 300. Find the difference between the cost of a book and a pen.

(a) Rs. 30

(b) Rs. 20

(c) Rs. 10

(d) None of these

8. The present average age of a couple and their daughter is 35 years. Fifteen year from now, the age of the number will be equal to the sum of present ages of the father and the daughter. Find the present age of the mother.

(a) 43 years

(b) 40 year

(c) 48 years

(d) 45 years

9. The cost of three pens, four erasers and ten sharpeners is Rs. 75. The cost of six pens. Seven erasers and twenty sharpeners is Rs. 146. Find the cost of each eraser.

(a) Rs. 3

(b) Rs. 4

(c) Rs. 5

(d) Rs. 6

10. Shyam and Ram have some chocolates with each of them, if shyam gives 5 chocolates of Ram, both will have equal number of chocolates. If Ram gives the same number of chocolates to shyam, shyam would have twice as many chocolates as Ram. Find the number of chocolates Ram has.

(a) 25

(b) 30

(c) 35

(d) 20

ANSWERS AND SOLUTION:

1.(a)

Let the number of Rs. 5 coins be x, Rs. 2 coins be y and Rs. 1 coins be Z.

x + y + z = 52 ………………….. (1)

5x + 2y + z = 125 …………………… (2)

x + y = 10 …………..(3) (2) ……….(1)

Gives that 4x + y = 73

x + y = 37

3x = 36

x = 36/3=12

Number of Rs. 5 coins = 12

2.(b)

Let the age of A, B and C be a, b and c respectively.

a + b = 4/3c, b = 2/3c

a + b + c = 35 = 4/3c + c = 35

7/3c = 35

C = 15, b = 2/3c = 10.

3.(b)

P = 3480/4 = 870

Q = 3480/5 = 696

R = 3480/6 = 580

P + Q + R = 870 + 696 + 580 = 2146

S = 3480 – 2146 = 1334

4.(b)

Let the number of marbles with Ajay and Vijay initially be A and V. If Vijay gives x marble to Ajay then vijay and Ajay would have V – x and A + x marbles respectively.

V – x = A + x …………………….. (1)

If Ajay gives 2x marble to Vijay then Ajay and Vijay would have A – 2x and V + 2x marbles respectively.

V + 2x –(A-2x) = 30 = V – A + 4x = 30 ……………… (2)

From (1) we have V – A = 2x

Substituting V – A = 2x in equation (2)

6x = 30 = x = 5.

5.(d)

Total distance travelled = 1800 km

Distance travelled by plane = 600 km

Let distance travelled by bus = x

Distance travelled by train = 3x/5

x + 3x/5+ 600=1800

8x/5=1200=x=750 km

6.(b)

Let the cost of each orange and each banana be a and b respectively.

12a + 18b = 84

If the cost of each orange doubles, it becomes 2a

6(2a) + 16b = 80

12a + 16b = 80

Substracting equation (2) from (1) we get 2b = 4

7.(b)

Let the price of book be y and price of pen be x.

x + 2y = 70

3x + 9y =300

By solving the equations we get x = 10 and y = 30

The difference between the cost of book and pen is 30 – 10 = Rs. 20

8.(d)

Let the present age of the father, mother and daughter be f, m and d respectively.

(f+m+d)/3=35

f + m + d = 105 …………………….. (1)

m + 15 = f + d

Substituting f + d as m + 15 in (1), we get 2m + 15 = 105

2m = 90 =m = 45 years

9.(b)

Let the cost of each pen, eraser and sharpener b p, e and s respectively.

3p + 4e + 10s = 75

6p + 7e + 20x = 146

Multiplying the first of the above equations by 2 and subtracting the second equation from it, we get e = 4

10.(a)

Let the number of chocolates with shyam and Ram be S and R respectively. If Shyam gives 5 chocolates to Ram, he would have S – 5 chocolates and Ram would have R + 5 chocolates.

So S – 5 = R + 5

S – R = 10 …………………… (1)

If Ram gives 5 chocolates to Shyam, he would have R – 5 chocolates and Shyam would have S + 5 chocolates.

S + 5 = 2 (R – 5)

2R – S = 15

Adding (1) and (2) we get R = 25.

Number of chocolates with Ram = 25

### Find solutions for all the questions at the end of each set:

### Set B

For Question (1-5) Find the odd no. in this Series.

1)60, 48, 38, 28,24,20,18

A)28

B)60

C)48

D)20

2)380, 188, 92,48,20,8,2

A)380

B)188

C)92

D)48

3)3, 4.5, 9, 22.5, 67.5, 270, 945

A)67.5

B)270

C)945

D)3

4)7, 8, 17, 42, 91, 172, 293

A)17

B)42

C)172

D)None of these

5)5, 15, 30, 135, 405, 1215, 3645

A)5

B)15

C)30

D)135

6)A tank is filled in 5 hours by three pipes A, B and C. The pipe C is twice as fast as B and B is twice as fast as A. How much time will pipe A alone take to fill the tank?

A)20 hours

B)25 hours

C)30 hours

D)35 hours

7)A man walked diagonally across a square lot. Approximately, what was the percent saved by not walking along the edges?

A)30

B)35

C)40

D)45

8)The average of 20 numbers is zero. Of them, at the most, how many may be greater than zero?

A)0

B)1

C)19

D)Can’t be determined

9)A train passes a station platform in 36 seconds and a man standing on the platform in 20 seconds. If the speed of the train is 54 km/hr, what is the length of the platform?

A)120 m

B)400 m

C)240 m

D)450 m

10)In one hour, a boat goes 11 km/hr along the stream and 5 km/hr against the stream. The speed of the boat in still water (in km/hr) is:

A)8 km/hr

B)10 km/hr

C)5 km/hr

D)15 km/hr

Answers with Explanation :

1. A

2. D

3. B

4. D

5. C

6. D

7. A

8. C

9. C

10.A

Explanation:

1. 60-12=48

48-10=38

38-8=30

30-6=24

24-4=20

20-2=18

So 28 is odd no. in this series.

2.380-192=188

188-96=92

92-48=44

44-24=20

20-12=8

8-6=2

So 48 is odd no. in this series.

3. 3*1.5=4.5

4.5*2=9

9*2.5=22.5

22.5*3=67.5

67.5*3.5=236.5

236.5*4=945

So 270 is odd no. in this series.

4. 7+1^2=8

8+3^2=17

17+5^2=42

42+7^2=91

91+9^2=172

172+11^2=293

So 9 is wrong no. in this series.

5. 5*3=15

15*3=45

45*3=135

135*3=405

405*3=1215

1215*3=3645

So 30 is odd no. in this series.

6. Pipe A+B+C take 5 hour to fill the tank.

and B=2A & C=2B = 4A

So A+B+C= 5hour

by put value 4A+2A+A= 5hour

7A take time 5 hour

A alone will take = 7*5= 35 hour

7. {2-(2)^1/2}/2 * 100 = 30 % approx

8. 19

9. train crosses the man in 20 sec.

so lenth of train / speed of train in m/sec = 20 sec

L/(54*5/18)= 20 ; Lenght of train= 300 m

now lengh of train+ platform/ (54*5/18)= 36 sec

on solving Lengh of Platform = 240 m

10. let boat speed = x; stream speed= y

11/(x+y)= 1 hour ; 5/ (x-y) = 1 hour

on solving x= 8km/hour

So Speed of Boat = 8 km/hr

### Find solutions for all the questions at the end of each set:

### Set C

1.If (a –1) +4/(a+3) = 0,find the value of (a+3)^3+ (a+2)^2

(a) 9

(b) 11

(c) 13

(d) 15

2.If α is an acute angle and 4tanα + 3cotα =7 , where α≠π/4 then the vlue of 2α is _______ .

(a) π

(b) Sin^(-1)(7/√50 )

(c) Sin^(-1)(7/25)

(d) Sin^(-1)(24/25)

3.A metallic cuboid of dimensions 45 cm ×25 cm ×24 cm is melted to form a cube. What is the total surface area of the cube?

(a) 4800 sq.cm

(b) 5400 sq.cm

(c) 5700 sq.cm

(d) 6400 sq.cm

4.A number is subtracted from its square resulting in 2162. The number is ______________ .

(a) 39

(b) 43

(c) 47

(d) 51

5.A sum of Rs.22,500 is borrowed at 25% p.a, simple interest. The sum is to be rapid in two equal installments in two years at the end of each year. The repayment to be made each year is ___________ .

(a) Rs.12,000

(b) Rs.15,000

(c) Rs.16,000

(d) Rs.18,000

6.If a and b are rational numbers satisfying a+√b = 3+2√2, then the value of b-√a is ______________________ .

(a) 8- √3

(b) 4+ √3

(c) 8- 2√3

(d) 4- 2√3

7.If an auditorium, there were 80 men and 60 women present just before the show started. During the show, five men left. The number of women present in the auditorium at the end of the show as a percentage of the total number of persons present in the auditorium is ___________ .

(a) 30%

(b) 36 2/3%

(c) 44 4/9%

(d) 49 1/9%

8.If tanϴ+cotϴ=8sinϴ cosϴ and 0 ≤ ϴ ≤ π/4,then find the value of sin4ϴ+cos4ϴ.

(a) -1

(b) 0

(c) 1

(d) ½

9.The LCM of two positive integers is 66 times their HCF. The sum of the LCM and the HCF is 3015. One of the integers is 45. Find the other integer.

(a) 1350

(b) 2250

(c) 2970

(d) 2880

10.Find the length of the radium of the in circle of an equilateral triangle whose side is 12√3 cm.

(a) 3√3 cm

(b) 3√6 cm

(c) 6 cm

(d) 3√2 cm

ANSWES AND SOLUTION:

1(a)

Given that (a – 1) + 4/(a+3 )=0

=>(a – 1) (a + 3) + 4 = 0

=>a^2 + 2a+1=0

=(a+1)^2=0 so a = -1

(a+3)^3+ (a+2)^2= (-1+3)^3+ (-1+2)^2

=(2)^3 + (1)^3 = 8+1=9

2(d)

3(b)

The volume of the cuboid is 45x25x24=27,000 cu.cm.

Let a be the side of the cube,

=>a^3= 27000 cu.cm

=> a = 30 cm

The total surface area of the cube is 6(a)^2

=6(30)^2= 5400 sq.cm

4(c)

Let the number be ‘n’

=>From the given information n^2 – n=2162

=>n(n-1) = 2162=2300-138=23(100-6)=23x2x47

=>n(n-1) = 47×46

comparing both sides, n = 47

5(b)

Let Rs. y be paid at the end of each year.

The amount at the end of two years

=Rs.22,500(1+(2×25)/100)= 22500(1.5)

y(1.25)+y = 22,500(1.5)

=> y = 15,000

6(a)

Given that a+√b = 3+2√2

=>a+√b = 3+√8,

a=3,b=8

so b-√a = 8-√3

7(c)

Total number of men and women in the audiotorium initially = 80+60=140

After five men left the number of men and women = 75+60=135

so The requied percentage = 60/135 x 100% = 44 4/9%

8(c)

9(c)

Let the HCF be x.

LCM = 66x

LCM + HCF = 3015

66x + x = 3015 => x = 45

Product of any two positive integers= Their LCM x Their HCF.

so 45(other integer) = (66x)(x)

other integer = (66*45*45)/45 = 2970

10(C)