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

### Set A

1.The breadth of a rectangular hall is three-fourths of its length. If the area of the floor is 768 sq.m. then the difference between the length and breadth of the hall is :

(1) 8 meters

(2) 12 meters

(3) 24 meters

(4) 32 meters

2.A is thrice as good as workman as B and therefore, able to finish a job in 60 days less than B. Working together they will do it in:

(1) 20 days

(2) 22 1/2 days

(3) 25 days

(4) 30 days

3.Two pipes A and B can fill a tank in 20 minutes and 30 minutes respectively. If both pipes are opened together, the time taken to fill the tank is:

(1) 50 minutes

(2) 12 minutes

(3) 25 minutes

(4) 15 minutes

4.If a man walks 20 km at 5 km/hr, he will be late by 40 minutes. If he walks at 8 km per hr, how early from the fixed time will he reach?

(1) 15 minutes

(2) 25 minutes

(3) 50 minutes

(4) 11/5 minutes

5.The distance between two cities A and B is 330 km. A train starts from A at 8 a.m. and travels towards B at 60 km/hr Another train starts from B at 9 a.m. and travels towards A at 75 km/hr at what time do they meet?

(1) 10 a.m.

(2) 10 : 30 a.m.

(3) 11 a.m.

(4) 11 : 30 a.m.

6.If AB is chord of a circle. P and Q are the two points on the circle different from A and B, then :

(1) The angles subtended at P and Q by AB are always equal.

(2) The sum of the angles subtended by AB at P and Q is always equal to two right angles

(3) The angles subtended by AB at P and Q are either equal or supplementary

(4) The sum of the angles subtended at P and Q is four right angles

7.A person who spends 66 2/3% of his income is able to save Rs. 1,200 per month. His monthly expenses (in Rs) is :

(1) 1,200

(2) 2,400

(3) 3,000

(4) 3,200

8.If cos 2x = cos 60° cos 30° + sin 60° sin 30°, then x is :

(1) 10°

(2) 15°

(3) 30°

(4) 45°

9.Applied to a bill for Rs. 1, 00, 000 the difference between a discount of 40% and two successive discounts of 36% and 4% is:

(1) Nil

(2) Rs. 1, 440

(3) Rs. 2,500

(4) Rs. 4, 000

10.Compound interest (compounded annually) on a certain sum of money for 2 years at 4% per annum is Rs. 102. The simple interest on the same sum for the same rate and for the same period will be:

(1) Rs. 99

(2) Rs. 101

(3) Rs. 100

(4) Rs. 98

Answer and Solution:

(1) Let the length of rectangular hall = xm

Breadh = 3/4 * xm

we know that Area of rectangular = Length * Breadth

= x * 3/4 x sq.m = 3/4 x^2 m^2

According to question.

3/4 x^2 = 768

x^2 = (768 * 4) / 3

or, x = √((768 ×4)/3) = 32m

Lenth = 32 cm and Breadh = 24 m

Required difference = 32 – 24 = 8m

(2) Let A can finish the whole work in x days

so B can finish the same work in 3x days.

According to question.

3x – x = 60

so x = 30 days

so A can finish the work in 30 days and B can finish the same work in 90 days.

so (A + B)’s one day’s work = 1/30 + 1/90 = 4/90

so (A + B)’s can finish the complete work in = 90/4 = 22 1/2 days.

3.(2) Required time = 1/(1/20+ 1/30)= (20 ×30)/50 = 12 minutes

4.(3) Time taken to cover 20 km at the speed of 5km/hr = 4 hours.

Fixed time = 4 hours – 40 minutes = 3 hours 20 minutes

Time taken to cover 20 km at the speed of 8 km/hr

= 20/8 = 2 hours 30 minutes

Required time = 3 hours 20 minutes – 2 hours 30 minutes = 50 minutes

5.(3) Distance travelled by first train in one hour = 60 * 1 = 60 km

A————————————–B

300km

Therefore, distance between two train at 9 a.m.

= 330 – 60 = 270 km

Now, Relative speed of two trains = 60 + 75 = 135 km/hr

Time of meet of two trains = 270/135 = After 2 hrs.

Therefore,both the trains will meet at 9+2= 11A.M.

6.(3) There are two possibilites :

Case I. When P and Q are on the same side of AB. In this case ∠APB= ∠AQB (angles in the same segment)

Cast II. When P and Q are on the opposite side of AB. In this case PAQB is a cycle quadrilateral.

So, ∠APB+ ∠AQB=180°

7.(2) Saving = 100% – 66 2/3%

= 33 1/3%

so 33 1/3% = Rs. 1200

so 100% = 1200/100 * 3 * 100

Rs. 3600

so Expenses = 3600 – 1200

= Rs. 2400

8.(2) cos 2x = cos 60° cos°30° + sin 60° sin 30°

= cos (60° – 30°)

= cos 2x = cos 30°

= 2x = 30 = x = 15°

9.(2) Successive discount of 36% and 4%

= {36 + 4 – (36*4)/100}%

= 38.56%

Difference = 40 – 38.56

= 1.44%

10.(3) Let principal be Rs. P

According to question.

102 = p {(1+r/100)^t- 1}

Where r = 4% and t

= 2 years

P = 102/((26/25)^2- 1)=Rs.1250

so Simple Interest at rate of 4% for 2 years

= (1250 ×4 ×2)/100=Rs.100

Required answer is Rs. 100

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

### Set B

1.In the solution of the multiplication question given below.’a’ is s digit.

a 2

× 7 a

=6396

The value of ‘a’ is

(1) 3

(2) 8

(3) 6

(4) 4

2. Lengths of the perpendiculars from a point in the interior of an equilateral triangle on its sides are 3 cm. 4 cm and 5 cm. Area of the triangle is

(1) 48 √3 cm^2

(2) 54 √3 cm^2

(3) 72 √3 cm^2

(4) 80 √3 cm^2

3. A man, a woman and a boy can complete a work in 20 days. 30 days and 60 days respectively. How many boys must assist 2 men and 8 women so as to complete the work in 2 days?

(1) 8

(2) 12

(3) 4

(4) 6

4. The measures (in cm) of sides of a right angled trinagle are given by consecutive integers. Its area (in cm^2) is

(1) 9

(2) 8

(3) 5

(4) 6

5. The average age of a husband and a wife was 27 years when they married 4 years ago. The average age of the husband, the wife and a new-born child is 21 years now. The present age of the build is

(1) 4 years

(2) 3 years

(3) 2 years

(4) 1 year

6. A reduction of 25% in the price of sugar enbles a man to buy 7 1/2 kg more sugar for Rs. 360. The original price per kg of sugar was.

(1) Rs. 16

(2) Rs. 18

(3) Rs. 20

(4) Rs. 25

7. A man buys some articles at Rs. P per dozen and sells them at Rs. P/8 per piece. His profit per cent is

(1) 30

(2) 40

(3) 50

(4) 60

8. A train with a uniform speed, crosses a platform, 162 metres long, in 18 seconds and another platform, 120 metres long, in 15 seconds. The speed of the train is

(1) 14 km/hr

(2) 42 km/hr

(3) 50.4 km/hr

(4) 67.2 km/hr

9. The number of boys and girls in a college are in the ratio of 3 : 2. If 20% of the boys and 25% of the girls are adults, the percentage of students, who are not adults, is

(1) 58

(2) 66 2/3

(3) 78

(4) 83 1/3

10. What sum of money at compound interest will amount to Rs. 650 at the end of one year and Rs. 676 at the end of 2 years?

(1) Rs. 520

(2) Rs. 572

(3) Rs. 600

(4) Rs. 625

SOLUTION

1. (2)

2. (1)

3. (3) Part of work done by 2 men and 2 women in 2 days.

= 2(2/20 + 8/30)

= 2(1/10 + 8/20) = 2((3+8)/30)

= 22/30 = 11/15

Remaining work = 1 – 11/15 = 4/15

work done by 1 boy in 2 days

= 2/60 = 1/30

4. (4) 3^2 + 4^2 = 5^2

Base = 3 cm

perpedicular = 4 cm

Area of the right angled triangle

= 1/2 * base * height

= 1/2 * 3 * 4 = 6 sq. cm.

5. (4) Sum of the present ages of husband and wife

= 2 * 27 + 8 = 62 years

Sum of the present ages of husband, wife and child

= 21 * 3 = 63 years

so present age of the child = 63 – 62 = 1 year

6. (1) Let the original price of sugar = Rs. x/kg

so New price of sugar

= x * 75/100 = Rs. 3x/4

According to the question.

360/(3x/4)- 360/x= 15/2

=480/x – 360/x=15/2

=120/x=15/2

x= (120 ×2)/15=16

7.(3) CP of each article

= Rs. P/12 and SP = Rs. P/8

Gain = P/8 – P/12 = (3P – 2P)/24 = P/24

so Gain per cent = P/(24/(P/12)) ×100=50%

8. (3) Let the Length of the train be x metre.

(x + 162)/18 = (x + 120)/15

Speed of the train

= (x + 162)/6 = (x + 120)/5

= 6x + 720 = 5x + 810

x = 810 – 720 = 90

Speed of the train

= (90 + 162)/18 m/sec

= 252/18 * 18/5 kmph = 50.4 kmph

9. (3)

10.(4)

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

### Set C

1.Clock A loses 1 minute a day and clock B gains 1 1/2 minutes a day. If clock B is 30 minutes ahead of clock A, how many days will clock B take to be 45 minutes ahead of clock A?

(1) 10

(2) 6

(3) 18

(4) 8

2.Which of the following equations are equivalent?

(a) 2p^2 – (3p^2 + 5) + 9 -2p^2 (p^2 – 1)

(b) (2p^2 + 3)^2

(c) (2p^2 – 3)^2

(d) 4p^2 + 12p^2 + 9

(1) Only a and b

(2) Only b and c

(3) Only b and d

(4) All except c

3.The population‘ of a town decreases every year due to death and migration by 5%. The population was 1 .20,000 last year. What will be the expected population at the end of the expected population at the end” of the next year?

(1)1,09,744

(2) 1,02,885

(3) l,O8,3O0

(4) Data inadequate.

4.Which of the following numbers is / are completely divisible by thirteen?

(a) 138138

(b) 121211

(c) 124214

(d) 120120

(1) All are divisible

(2) Only a and b

(3) Only b and d

(4) Only a and d

5.A certain tank can be filled by pipes A and B separately in 4 and 5 minutes respectively. Whereas, pipe C can empty it in 3 minutes. How long will it take to fill or empty the 4/5 full tank. If all the three pipes start together?

(1) 1 5/7 minutes to fill

(2) 6 6/7 minutes to fill

(3) 1 5/7 minutes to fill

(4) 6 6/7 minutes to fill

6.What will be the difference the interest obtained by investing Rs. 500/- for two years at the rate of 10% p.a. compounded yearly and Rs. 800/- at the rate of 10% p.a. compounded half-yearly for one year‘?

(1) Rs. 20

(2) Rs. 27

(3) Rs. 60

(4) Rs. 23

7.When a dealer heard that the price of certain product was about to increase Rs. 5 per pack, he purchased a number of packs of this product for Rs. 4,500/-. Had he pur- chased it at the new price, he would have obtained 10 fewer packs. How many packs did he buy’?

(1) 90

(2) 100

(3) 50

(4) 125

8.How many kilograms of coffee price at Rs. 33 per kg should be mixed with the coffee at Rs. 27 per kg so that the 60 kg of mixture costs Rs. 32 per kg?

(1) 30

(2) 20

(3) 50

(4) 10

9.If A and B work together, they complete a work in 3 days, B and C together complete the same work in 6 days, while A and C complete that work in 8 days. If there of them many will they complete the woek?

(1) More than 3 days

(2) More than 2 days

(3) Less than 3 days

(4) More than 4 days

10.If a rectangular space 8 cm long and 6 cm wide is increased in its lenght and width by 25%, then what will be the percentage increase in the area of original rectangular space?

(1) 25

(2) 50

(3) 36

(4) 56 1/4

SOLUTION

1.(2) According to question.

Clock B gains per hours to

A = (1/24 +1/16)

= (2 + 3) /48 = 5/48 minutes

Now.

Clock B gains 5/48 minutes in a hour

So Clock B gains 15 minutes in

48/5 * 15 hour

= (48 * 15)/(5 * 24) days = 6 days.

2.(5) (a) = 2P^2 (3p^2 + 5) + 9 – 2p^2 (P^2 – 1)

= 6p^4 + 10p^2 + 9 – 2p^4 + 2p^2

= 4p^2 + 12p^2 + 9

= (2p^2 + 3)^2

(b) = (2p^2 + 3)^2

(c) = (2p^2 – 3)^2

(d) = 4p^4 + 12p^2 + 9

= (2p^2 + 3)^2

so (a) = (b) = (d)

Therefore, the required answer is option (4).

3(2)According to question.

Population of town (last year) = 120,000

Present population of town

= 100000 – 5% of 120000

= 120000 – (5 * 120000)/100

= 120000 – 60000

= 114000

so Next year population of town

= 114000 – 5% of 114000

= 114000 – (5 * 114000)/100

= 114000 – 5700 = 108300

4.(4) (a) = 138138 ÷ 13 = 10626

(b) = 121211 ÷ 13 = 9323 12/13

(c) = 124214 ÷ 13 = 9554 12/13

(d) = 120120 ÷ 13 = 9240

Therefore, the required, answer is option (4).

5(1) A’s work in one minute = 1/4

B’s work in one minute = 1/5

C’s work in one minute = 1/3

so (A+B+C)’s work in one minute

= (1/4 + 1/5 – 1/3)

= (15 + 12 – 20)/60 = 7/60

so Time taken to fill 1-4/5

i.e. 1/5 part of tank

= 60/7 * 1/5 = 12/7 = 1 5/7 minutes

6.(4) From the Formula

A = P (1 + 10/100 )^t

in first case

A1 = 500 (1 + 10/100 )^2

= 500 * 110/100 * 110/100 = Rs. 605

so Compound Interest

= 605 – 500 = Rs. 105

so In second case

r = 10/2 = 5% half yearly

t = 1 * 2 = 2 half yearly.

so A2 = 800 (1 + 5/100 )^2

= 800 * 105/100 * 105/100

= 800 * 21/20 * 21/20 = Rs. 882

so compound Interest

= Rs. 882 = Rs. 800

= Rs. 82

so Required difference

= 105 – 82 = Rs. 23

7.(2) Let the number of purchased pack = x

so According to question.

4500/x = 4500/x -10 – 5

or, 4500 [1/(x )-1/(x – 10)] = -5

or, 900 [1/(x – 10) – 1/(x )] = 1

or, (900 [x – (x – 10) ])/((x – 10)x)= 1

or, 900 * 10 = x^2 – 10x

or , x^2 – 10x – 9000 = 0

or x^2 – 100x + 90x – 9000

= 0

or, x(0 – 100) + 90 (x -100)

= 0

or, (x + 90) (x – 100) = 0

or, x = – 90 and 100

Since the value of x should not be negative, therefore, the required answer is 100.

8.(3)

9.(1) work done by 2(A + B + C) in one day

= (1/3 +1/6+1/8 )

= (8 + 4 + 3)/24 = 15/24 = 5/8 part

so (A + B + C)’s one day work

= 5/8*2 = 5/16 work

so Whole work can be done by

(A + B + C) in 16/5 days i.e. 3 1/5 days

Therefore, the required answer is option (1).

10.(4)