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

### Set A

1.A pump can fill a tank with water in 2 hours. Because of a leak, it took 2 1/3hours to fill the tank. The leak can drain all the water of the tank in:

A.4 1/3hours

B.7 hours

C.3 9/17 hours

D.4 1/2 hours

2.A book was sold for Rs 27.50 with a profit of 10%. If it were sold for Rs. 25.75, then would have been percentage of profit and loss ?

A.2% Profit

B.3% Profit

C.2% Loss

D.3% Loss

3.How much time will it take for an amount of Rs. 900 to yield Rs. 81 as interest at 4.5% per annum of simple interest?

A. 2 years

B. 3 years

C. 1 year

D. 4 years

4.A sphere of radius 3cm is drawn into a wire of thickness of 0.5cm. What is the length of the wire?

A.146cm

B.144cm

C.148cm

D.154cm

5.A sphere of radius 7cm is cut into two equal halves.what is the volume of each of the halves?

A.718 2/3

B.718 3/2

C.719 2/3

D.719 3/5

6.What is the compound intrest on Rs.10000 at 40% p.a. for 9 months,intrest being compounded quartely?

A. 3310

B. 3610

C. 3340

D. 3320

7. Rahul sold his bycycle after offering 10% discount.If he had sold it after offering another discount of the same amount,his selling price would have been Rs.480 find his marked prices.

A. 640

B. 600

C. 700

D. 680

8.A can do a work in 6 days more than what B takes to do the work. A worked for 7 days, then B takes the work and completed it in 10 more days.In how many days each of them can complete the work individually?

A.A can 21 days and B can 15 days

B.A can 24 days and B can 17 days

C.A can 22 days and B can 16 days

D.A can 26 days and B can 15 days

9.12 men can do a work in 15 days working 8 hours a days. In how many days can 9 men do the same work, working 10 hours a days?

A. 20

B. 18

C. 16

D. 21

10. Find value of tan6°x tan42°x tan48°x tan84°

A. 1

B. 2

C. 3

D. 0

ANSWERS AND SOLUTION:

1.(D)Explanation:

Work done by the leak in 1 hour = (1/2-3/7)=1/14

SO Leak will empty the tank in 14 hrs.

2(B)Explanation:

S.P.=(100+gain%)/100 x C.P)

So, C.P. = (100/110x25.75)

When S.P. = 25.75 then

Profit=25.75-25=Re.0.75

Profit%=0.75/25x100=3%

3(A)Explanation :

P = Rs.900

SI = Rs.81

T = ?

R = 4.5%

T= (100×SI)/PR= (100×81)/(900×4.5)=2 years

4(B)Explanation:

Since the sphere is drawn into wire,volume of the sphere is equal to volume of the wire.4/3p(3)^3= p(5/10)^2xh

=>h=144cm

5(A)

6(A)

7(B)Explanation:

Let his marked price be x

SP = MP-Discount

so 480 = x-2(10/100)x

x = 600

8(A)Explanation:

Let B take x days to do the work.

A takes (x+6) days to do the work.

Workdone by A in 7 days. 7/x+6

Workdone by B in 10 days. 10/x

So 7/x+6 + 10/x =1

(7x+10x+60)/(x+6)(x) = 1

17x + 60=x^2+6x

=>x^2 - 11x-60 = 0

=>x^2-15x + 4x-60=0

=>x(x-15)+4(x-15)=0

=>x=15

A can do the 21 days and B can do 15 day.

9(C)Explanation:

We have M1D1H1 = M2D2H2

so 12x15x8 = 9xD2x10

D2 = 16days.

10(A)

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

### Set B

1.The ratio of the areas of two isosceles triangles having equal vertical angles is 1 : 4. The ratio of their heights will be

(1) 1 : 2

(2) 3 : 4

(3) 2 : 3

(4) 6 : 7

2.If each of the radius of base and height of a right circular cone is increased by 10%, then the percentage of increase in the volume of the cone will be

(1) 20

(2) 33. 1

(3) 44.2

(4) 100

3.While selling a shirt, a shopkeeper gives a discount of 7%. If he had given a discount of 9% he would have got Rs. 15 less as profit. The marked price of the shirt is

(1) Rs. 750

(2) Rs. 720

(3) Rs. 712.50

(4) Rs. 600

4. A person went from A to B at an average speed of x km/hr and returned from B to A at an average speed of y km/hr. What was his average speed during the total journey?

(1) x + y/2xy

(2) 2xy/x + y

(3) 2/x+y

(4) 1/x + 1/y

5. The average monthly salary of A and B is Rs. 14000, that of B and C is Rs. 15600, and that of A and C is Rs. 14400. Monthly salary of B is

(1) Rs. 12400

(2) Rs. 12800

(3) Rs. 15200

(4) Rs. 16000

6. In an examination 42% students failed in Hindi and 52% failed in English. If 17% failed in both of these subjects, the percentage of students who passed in both the subjects, was

(1) 23

(2) 27

(3) 34

(4) 40

7.A reduction of 20% in the price of apples enables a man to buy 16 kg more apples for Rs. 4000. What is the reduced price per kg of apples?

(1) Rs. 64

(2) Rs. 60

(3) Rs. 50

(4) Rs. 40

8. Two numbers are less than a third number by 30% and 37% respectively. The per cent by which the second number is less than the first is

(1) 10

(2) 7

(3) 4

(4) 3

9. A is twice as fast runner as B, and B is thrice as fast runner as C. If C travelled a distance in 1 hour 54 minutes, the time taken by B to cover the same distance is

(1) 19 minutes

(2) 38 minutes

(3) 51 minutes

(4) 57 minutes

10.A lent Rs. 5000 to B for 2 years and Rs. 3000 to C for 4 years at simple interest at the same rate of interest. He received Rs. 2200, in all, from both of them as interest. The rate of interest perannum was

(1) 5%

(2) 7%

(3) 8%

(4) 10%

ANSWERS AND SOLUTION:

1.(1) The areas of two similar triangles are in the ratio of square of their corresponding altitudes.

2.(2) Volume of the cone = 1/3 πr^2 h

Effective change of 10% and 10% =

= {10 + 10 + (10 * 10)/100} = 21%

Effective change of 21% and 10%

= {21 + 10 + (21 * 10)/100}% = 33.1%

3.(1) Let the marked price of the shirt be Rs. x.

Difference of discounts = 2%

SO 2% of x = 15

=>(x * 2)/100 = 15

=> x = (15 * 100)/2 = Rs. 750

4.(2)

5.(3) A + B + C = Rs. 2/2 (14000 + 15600 + 14400) = Rs. 44000

A + C = Rs. (2 * 14400)

= Rs. 28800

SO B = Rs. (44000 – 28800)

= Rs. 15200

6.(1) Percentage of students who failed in Hindi or English or both = 42 + 52 – 17 = 77%

SO Percentage of students who passed

= 100 – 77 = 23%

7.(3) let the original price of apple = Rs. x per kg

New price = Rs. 4x/5

SO 4000 * 5 /4x – 4000/x = 16

=>1000/x = 16

=>X = 1000/16 = 62.5

SO New price = 4/5x

= Rs. (4/5 * 62.5)

New price = 4/5x

= Rs. 50 per kg

8.(1) Third number = 100

First number = 70

Second number = 63

SO Required percentage = 7/70 * 100 = 10

9.(2) Ratio of the speeds of A and B

= A : B = 2 : 1 = 6 : 3

B : C = 3 : 1

so A : B : C = 6 : 3 : 1

Ratio of their time taken

=1/6 : 1/3 : 1

so Time taken by B

= (2/6 * 114) minutes

= 38 minutes

10.(4) (5000 * 2 * R)/100 + (3000 * 4 * R) /100

= 2200

= 100R + 120R = 2200

= 220R = 2200

= R = 2200/220 = 10%

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

### Set C

1.A path of uniform width surrounds a circular park. The difference of internal and external circumferences of this circular path is 132 metres. Its width is: (Take π=22/7)

A.22m

B.20 m

C.21m

D.24m

2.A train 800 metre long is running at the speed of 78 km/hr. If it crosses a tunnel in 1 minute, then the length of the tunnel (in metres) is :

A.77200

B.500

C.1300

D.13

3.A man rows a boat 18 kilometres in 4 hours downstream and returns upstream in 12 hours. The speed of the stream (in km per hour) is:

A.1

B.1.5

C.2

D.1. 75

4.8% of the voters in an election did not cast their votes. In this election, there were only two candidates. The winner by obtaining 48% of the total votes defeated his contestant by 1100 votes. The total number of voters in the election was:

A.21000

B.23500

C.22000

D.27500

5.A, B and C start at the same time in the same direction to run around a circular stadium. A completes a round in 252 seconds, B in 308 seconds and C in 198 seconds, all starting at the same point. After what time will they next meet at the starting point again?

A.46 minutes 12 seconds

B.45 minutes 12 seconds

C.42 minutes 36 seconds

D.26 minutes 18 seconds

6.A trader marks his goods at 20% above the cost price. If he allows a discount of 5% on the marked price, what profit per cent does he make?

A.14%

B.16%

C.18%

D.20%

7.8 men can do a work in 12 days. After 6 days of work, 4 more men were engaged to finish the work. In how many days would the remaining work be completed?

A.2

B.3

C.4

D.5

8.In an alloy, the ratio of copper and zinc is 5 : 2. If 1.250 kg of zinc is mixed in 17 kg 500 g of alloy, then the ratio of copper and zinc will be

A.2 : 1

B.2 : 3

C.3 : 2

D.1 : 2

9.The simple interest on a certain sum for 8 months at 4% per annum is Rs. 129 less than the simple interest on the same sum for 15 months at 5% per annum. The sum is :

A.Rs. 2,580

B.Rs. 2400

C.Rs. 2,529

D.Rs. 3600

10.40 liters of a mixture of milk and water contains 10% of water, the water to be added, to make the water content 20% in the new mixture is :

A.6 litres

B.6. 5 litres

C.5.5 litres

D.5 litres

ANSWERS AND SOLUTION:

1. (3) Let the internal radius of the park be r and the external radius (with the path) be R.

The difference between the internal and external circumferences is 132m.

so 2πR-2πr = 132

=>2π(R-r) = 132

=R – r = 132/2π

= (132 * 7)/(2 * 22) = 21

Hence, the width of path

= 21 metres

2.(2)

3.(1) Rate downstream

= 18/4 = 9/2 kmph

Rate upstream = 18/12 = 3/2 kmph.

Now, speed of the stream

= (Rate downstream – Rate upstream)/2

=((9/2)-(3/2))/2=6/4 =3/2 =1.5kmph

4.(4) Let the total number of votes be 100.

Number of uncast votes = 8

so Number of votes obtained by the winner = 48

Number of votes obtained by the loser = 48 – 44 = 4

If the difference of win be 4 votes, total voters = 100

so When the difference be 1100 votes, total voters

= 100/4 * 1100 = 27500

5.(1) Required time = LCM of 252.

308 and 198 seconds.

Now, 252 = 2 * 2* 3 * 3 * 7

308 = 2 * 2 * 7 * 11

198 = 2 * 3 * 3 * 11

so LCM = 2 * 2* 3 * 3 * 7 * 11

= 36 * 77 seconds

= (36 * 77)/60 minutes

= 231/5 = 46 minutes 12 seconds

6.(1) Let the cost price = Rs. x

Marked price = x + 20% of x

= x + x/5 = Rs. 6x/5

Selling Price

= Rs. (6x/5 – 5% of 6x/5)

= Rs. 6x/5 (1 – 1/20)

= Rs. 6x * 19/20

= Rs. 57x/50

Profit = 57x/50 – x = Rs. 7x/50

Profit% 7x/50/x * 100 = 14%

7.(3) Work done by 8 men in 6 days

= 6/12 = 1/2

Remaining work = 1 –1/2 = 1/2

4 more men are engaged.

Total number of men

= 8 + 4 = 12

By work and time formula

W1/M1D1= W2/M2D2, we have

1/8*12 = ½/(12 * D2)

= D2 = ½ * 8 * 12/12

= 4 days

8.(1) Weight of copper in 17 kg 500 gm i.e. 17500 gm of alloy

= 5/7 * 17500 = 12500 gm

Weight of zinc = (17500 – 12500)

= 5000 gm

1250 gm of zinc is mixed in alloy.

Total weight of zinc

= 1250 + 5000 = 6250 gm.

Required ratio

= 12500 : 6250 = 2 : 1

9.(4) Let the sum be Rs. x

(x * 5 * 15)/(100 * 12) – (x * 4 * 8)/(100 * 12) = 129

= x/(100 * 12) (75 - 32) = 129

X = (129 * 1200)/ 43

Rs. 3600

10.(4) Water content in 40 litres of mixture = 40 * 10/100

4 litres.

so Milk content = 40 – 4

36 litres

Let x litres of water is mixed.

(4 + x)/(40 + x) = 20/100

(4 + x)/ (40 + x) = 1/5

=20 + 5x = 40 + x

4x = 20

X = 5 litres

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