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

### Set A

(1) The least five-digit perfect square number which is divisible by 3,4,5,6,8 is

a.14400

b.10800

c.10201

d.32400

(2) Which of the following numbers does not fit into the series?

14,19,29,40,44,51,59,73

a.59

b.51

c.29

d.44

(3) By selling a table for Rs.30,a shopkeeper gains 20%.During a clearance sale,the shopkeeper allows a discount of 10% on the marked price.His gain percentage during the sale season is

a.7.5

b.8

c.7

d.9

(4) From a vessel containing 100L of wine, 10L are drawn out and an equal amount of water is added. From the mixture, 10L is again drawn out and same quantity of water is added.What is the final ratio of wine to water?

a.90:10

b.91:9

c.81:19

d.80:20

(5) The marks of 3 students A,B and C are in the ratio of 10:12:15.If the maximum marks of the paper are 100,then the marks of B cannot be in the range of

a.40-50

b.70-80

c.20-30

d.80-90

(6) Mukesh uses 920 g in place of 1 kg to sell his goods.When he sells his article at 15% gain on the cost price,the actual percentage of profit is

a.15

b.25

c.30

d.20

(7) From a circular sheet of paper of radius 10 cm,a sector of area 40% is removed.If the remaining part is used to make a conical surface,then the ratio of the radius and the height of the cone is

a.1:1

b.1:2

c.4:3

d.3:4

(8) If x=sinθ+cosθ and y = secθ+cosecθ,find y in terms of x

a.2x/x^2+1

b.2x/x^2-1

c.x/x^2+1

d.x/x^2-1

(9) If sinθ +cosec θ =2,then the value of sin^7θ+cosec^2 θ is

a.1/2

b.2

c.0

d.1

(10) The maximum value of sin^8 θ + cos^14 θ,for all real values of θ is

a.1

b.0

c.2

d.1/2

ANSWERS

(1)A

LCM of 3,4,5,6 and 8=120.Now,by seen the option we get that 14400 is a least five digit perfect square number which is divisible by 120

(2)B

it follows 1+4,next one 1+9,2+9 in same way 44+(4+4)=52 not 51

(3)B

given S.P of table =30 profit percentage = 20% CP of table =(30*90)/10 =27 required profit percentage = (27-25)/25 *100 =8%

(4)C

Here, a=10L, n=2 and x=100L

Quantitiy of wine in end =x(1-a/x)^n

=100(1-10/100)^2

=81L

Required ratio =81:(100-81)=81:19

(5)D

Let the marks of A,B and C are 10x,12x and 15X respectively.

maximum marks of C=15*6=90 and maximum marks of

b=12*6=72 hence the marks of B cannot be in the range of (80-90)

(6)B

Let CP=Rs 1000

Actual CP=Rs 920 and selling price =(1000*115)/100 = 1150

Actual profit percentage = (1150-920)/920 * 100% =25% ans

(7)D

Perimeter of circular sheet = 2πr =20π cm

The perimeter of base of conical surface = 20π*(100-40)/100 =12π

Radius of base of conical surface = 12π/2π = 6cm

& the height of conical surface = √(10^2-6^2)=8cm

so,The required ratio = 6:8 or 3:4

(8)B

x= sinθ+cosθ y= Secθ+cosecθ

=1/sinθ+1/cosθ

=sinθ+cosθ/sinθcosθ

=x/sinθcosθ……..2

(sinθ+cosθ)^2=1+2sinθcosθ

x^2=1+2sinθcosθ

sinθcosθ=(x^2-1)/2 from equation …..2

y=2x/x^2-1 ans

(9)B

sinθ+cossecθ=2

sinθ+1/sinθ =2

sin^2θ+1=2 sinθ

(sin^2θ-2sinθ+1)=0

(sinθ-1)^2=0

sinθ=1=sin90°

θ = 90°

so,sin^7θ+cosec^7θ=1+1 =2ans

(10)A

f(θ)=sin^8θ+cos^14θ

=sin^8θ+(1-sin^2θ)^7

f(90°)=1+(1-1)^7

=1

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

### Set B

1. In an examination P scored 25 marks less than Q. Q scored 45 more marks than R. T scored 75 marks which is 10 more than R. U’s score is 80 less than maximum marks of the test. What approximate percentage of marks did U score in the examination if he gets 55 marks more than Raman?

(1) 90

(2) 70

(3) 80

(4) 60

2. Two pipes A and B can fill a tank independently in 10 hours and 15 hours respectively, while pipe C can empty it in 30 hours. All pipes are kept open for 6 hours after which pipes B and C are closed. In what time now onwards would the tank get full?

(1) 6 hours

(2) 2 hours

(3) 2.5 hours

(4) 3 hours

3. The largest and the smallest angles of a triangle are in the ratio of 3:1 respectively. The second largest angle of the triangle is equal to 56°. What is the value of largest angle of the triangle?

(1) 49

(2) 129

(3) 123

(4) 93

4. Fifteen men take 21 days of 8 hours each to do a piece of work. How many days of 6 hours each would 21 women take if 3 women do as much work as 2 men?

(1) 20

(2) 21

(3) 25

(4) 30

5. John purchased an item for Rs. 52,000 and sold it at loss of 25 percent. With that amount he purchased another item and sold it at a gain of 40 percent. What was his overall gain/loss ?

(1) Loss of Rs. 2600

(2) Profit of Rs. 2600

(3) Loss of Rs. 6200

(4) Profit of Rs. 6200

6. In a school, there are 3600 students. The ratio of boys to girls is 4 : 5. If twenty percent of the boys and sixty percent of the girls like to play hockey, then how many students do not like to play hockey?

(1) 1520

(2) 1250

(3) 2008

(4) None of these

7. The ratio of the present ages of Sonu and Monu is 7: 6 respectively. Eight years ago the respective ratio of their ages was 5 : 4. What will be Monu’s age four years from now?

(1) 28 years

(2) 32 years

(3) 24 years

(4) 30 years

8. The sum of three consecutive odd numbers is 20 more than the smallest number. What is the middle number?

(1) 7

(2) 9

(3) 11

(4) 5

9. A invests Rs. 24000 to start a business. Four months later B joins him by investing Rs. 31000 and after another two months C joins them by investing Rs. 40000. At the end of one year the business earns a profit of Rs. 12028. What is C’s share in the profit?

(1) Rs. 4464

(2) Rs. 3844

(3) Rs. 3720

(4) Rs. 3270

10. 2 men can complete a piece of work in 6 days. 2 women can complete the same piece of work in 9 days, whereas 3 children can complete the same piece of work in 8 days. 3 women and 4 children worked together for 1 day. If only men were to finish the remaining work in 1 day, how many total men would be required?

(1) 4

(2) 8

(3) 6

(4) 2

Answers with Explanation:-

1.(4) Marks of T = 75

Marks of R = 65

Marks of Q = 110

Marks of P = 85

Marks of U = 120

Maximum marks = 200

Required percentage = 120/200 x 100 = 60%

2.(2)Let the capacity of the tank be 30 litres.

So Pipe A can fill 3 litre/hour, Pipe B can fill 2 litre/hour and Pipe C can empty 1 litre/hour.

Together they can fill = 3 + 2 – 1 = 4 litre/hour

Tank filled in 6 hours = 24 litres

Time to fill the remaining tank by pipe A alone = 6/3 = 2 hours

3.(4)Let the largest and smallest angles be x and 3x. Now

x + 3x + 56 = 180

x = 31

largest angle = 93°.

4.(4)3W = 2M

21 W = 14 M

Let the required number of days be x.

N1 D1 H1 = N2 D2 H2

15 X 21 X 8 = 14 X 6 X x

X = 30 days

5.(2)CP of first item = Rs. 52000

Selling price of second item = 52000 x 0.75 x 1.4

His overall profit = 54600 – 52000 = 2600

6. (4)

Total Students in school = 3600

Number of boys = 4/9 x 3600 = 1600

Number of boys who like hockey = 20% of 1600 = 320

Number of girls = 2000

Number of girls who like hockey = 60% of 2000 = 1200

Number of students who do not like hockey = (1600 – 320) + (2000 – 1200) = 2080

7. (1)

Let the present ages of Sonu and Monu be 7x and 6x. Now

7x – 8 /6x – 8 = 5/4

x = 4

Present age of Monu = 24 years

Monu’s age four years from now = 24 + 4 = 28 years

8. (2)

Let the numbers be x, x + 2 and x + 4. Then

x + (x + 2) + (x + 4) = x + 20

x = 7

So the middle number is 9.

9. (3)

The ratio of their investments = 24000 x 12: 31000 x 8 : 40000 x 6 = 36 : 31:30

Since the ratio of investment is also the ratio of profit,

C’s share = 30/97 x 12028 = 3720

10. (2)

2 M x 6 = 2 W x 9 = 3 C x 8

2 M = 3 W = 4 C

The ratio of efficiency of man, woman and children = 1/2: 1/3: 1/4 = 6: 4: 3

Let the work done by a man, a woman and a children in one day be 6 units, 4 units and 3 units respectively.

So the total work to be done = 2x6x6 = 72 units

Work done by 3 women and 4 children in one day = 3 x 4 + 4x 3 = 24 units

Remaining work = 72 – 24 = 48 units

Number of men required to complete the remaining work in one day = 48/6 = 8

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

### Set C

1. Anil, Mukesh and Ritesh started a business each investing Rs.20,000. After 4 month Anil withdraws Rs.6000, Mukesh withdraws Rs.8000, Ritesh invest Rs.6000 more At the end of the years, a total profit was Rs.65600. Find the share of Ritesh.

A. Rs. 20000

B. Rs. 28800

C. Rs. 17600

D. Rs. 19200

2. Joy started a business and he invested in 76000, After some month, amar came to join with him and invest 57000.The end of the year the total profit was divided among them into ratio form 2 : 1.Find after how many months amar join.

A. 4

B. 6

C. 8

D. 3

3. Samir started a software business by investing Rs. 40,000 . After six months , Nitish Joined him with a capital of Rs. 60,000 . After 3 years , they earned a profit of Rs . 27,900 . What was Samir’s share in the profit ?

A. Rs. 12400

B. Rs. 13000

C. Rs. 13200

D. Rs. 15000

4. Anil, Mukesh and Ritesh started a business by investing Rs. 125000 Rs. 150000 and Rs.175000 respectively. Find the share of Mukesh, out of an annual profit of Rs. 93,600..

A. Rs. 36400

B. Rs. 31200

C. Rs. 32500

D. Rs. 33200

5. Jon and Harry started a partnership business investing some amount of money in the ratio of 2 : 3 . Ron joined them after six months with an amount equal to that of Harry . In what proportion should the profit at the end of one year be distributed among Jon , Harry and Ron ?

A. 5:3:4

B. 4:6:2

C. 5:3:2

D. 4:6:3

6. Manoj received Rs. 6000 as his share out of the total profit of Rs. 9000 which he and Ramesh earned at the end of one year. If Manoj invested Rs.120000 for 6 months, whereas Ramesh invested his amount for the whole year, what was the amount invested by Ramesh?

A.Rs. 20000

B.Rs. 30000

C.Rs. 40000

D.Rs. 50000

7. Yogesh started a business investing Rs. 45000. After 3 months, Pranab joined him with a capital of Rs. 60000. After another 6 months, Atul joined them with a capital of Rs. 90000. At the end of the year, they made a profit of Rs. 20000. What would be Atuls share in it?

A.Rs 7000

B.Rs 6000

C.Rs 5000

D.Rs 4000

8. In business, A and C invested amounts in the ratio 2:1, whereas the ratio between amounts invested by A and B was 3:2, If Rs 157300 was their profit, how much amount did B receive?

A.Rs 48000

B.Rs 47000

C.Rs 47400

D.Rs 48400

9. Manoj got Rs.6000 as his share out of a total profit of Rs.9000 which he and Ramesh earned at the end of one year. If Manoj invested Rs.20,000 for 6 months, where as Ramesh invested his amount for the whole year, what was the amount invested by Ramesh ?

A. Rs.30000

B. Rs.40000

C. Rs.10000

D. Rs.5000

10. Rs.700 is divided among A,B and C so that A receives half as much as B and B half as much as C. Then C’s share is :

A. Rs.200

B. Rs.300

C. Rs.400

D. Rs.600

Answers with Explanation:-

1. (B):

Ratio capital of Anil, mukesh and Ritesh.

= ( 20,000 x 4 + 14000 x 8 ) : ( 20,000 x 4 + 12000 x 8 ) : ( 20,000 x 4 + 26000 x 8 )

= 192000 : 176000 : 288000

Anil share = (65600 x 192 / 656 ) = 19200

Mukesh share = ( 65600 x 176 / 656 ) = 17600

Ritesh share = (65600 x 288 / 656 ) = 28800

2. (A):

Step 1: we can assume that amar join into business after x months.So amar money was invest into (12 – x ) months.

Step 2: 76000 x 12 / 57000 x ( 12 – x ) = 2 / 1

912000 = 114000 ( 12 – x ) = 114 ( 12 – x ) = 912 = x = 4

After 4 months amar join the business.

3. (A):

Short tricks : Samir : Nitish share of capital

= ( 40,000 x 36 ) : ( 60,000 x 30 ) = 1440000 : 1800000 = 4 : 5 .

Samir’s share is = Rs . 27900 x 4 / 9 = Rs. 12400.

4. (B):

Ration of share Anil, Mukesh and Ritesh = Ratio of their investment

Anil : Mukesh : Ritesh = 125000 : 150000 : 175000 = 5 : 6 : 7

Anil share = Rs. [93600 x 5 / 18 ] = 26000.

Mukesh share = Rs. [93600 x 6 / 18 ] = 31200.

Ritesh share = Rs. [93600 x 7 / 18 ] = 36400

5. (D):

Short tricks : Let the initial investment money ratio of Jon and Harry is 2x and 3x So Jon , Harry and Ron ratio of investment is ( Jon : Harry : Ron ) = (2x X 12 ) : ( 3x X 12 ) : ( 3x X 6 ) = 24 : 36 : 18 = 4 : 6 : 3

6. (B):

Suppose Ramesh invested Rs. x. Then,

Manoj : Ramesh = 120000 * 6 : x *12.

720000/12x: 6000/3000

x = 30000

7. (D):

Just take care of the months of investment, rest all will be simple.

Yogesh:Pranab:Atul = 45000*12:60000*9:90000*3 = 2:2:1

Atul’s share = Rs. 20000 * (1/5) = Rs. 4000

8. (D):

A:B = 3:2 = 6:4

A:C = 2:1 = 6:3

A:B:C = 6:4:3

B share = (4/13)*157300 = 48400

9. (D)

Let the amount invested by Ramesh = Rs.x.Then, 20000×6 : 12x=6000:3000

or 12000012x=21 or x = 5000

10. (C)

Let C’s share = Rs.x. Then

B’s share = Rs.x2

And, A’s share = Rs.x4

A:B:C = x4:x2:x=1:2:4

Hence, C’s share = Rs.(700×47) = Rs.400