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

### Set A

1.A number divided by 68 gives the quotient 269 and remainder zero. If the same number is divided by 67, the remainder is :

(1) 0

(2) 1

(3) 2

(4) 3

2.If the sum and difference of two numbers are 20 and 8 respectively, then the difference of their squares is:

(1) 12

(2) 28

(3) 80

(4) 160

3.If ⋆ is an operating such that x ⋆ y = 3x + 2y, then 2 ⋆ 3 + 3 ⋆ 4 is equal to :

(1) 18

(2) 29

(3) 32

(4) 38

4.In a school, the average age of students is 6 years, and the average age of 12 teachers is 40 years. If the average age of the combined group of all the teachers and students is 7 years, then the number of students is :

(1) 396

(2) 400

(3) 408

(4) 416

5.The average age of 30 boys in a class is 15 years. One boy aged 20 years, left the class, but two new boys came in his place whose ages differ by 5 years. If the average age of all the boys now in the class still remains 15 years, the age of the younger newcomer is :

(1) 20 years

(2) 15 years

(3) 10 years

(4) 8 years

6.Given that 10% of A’s income = 15% of B’s income = 20% of C’s income. If sum of their income is Rs. 7800. Then B’s income is :

(1) Rs. 3600

(2) Rs. 3000

(3) Rs. 2400

(4) Rs. 1800

7.If two numbers are respectively 20% and 50% of a third number, what is the ratio between the two numbers ?

(1) 5 : 2

(2) 2 : 5

(3) 1 : 5

(4) 1 : 2

8.If a number x is 10% less than another number y and y is 10% more than 125, then x is equal to

(1) 150

(2) 143

(3) 140.55

(4) 123.75

9.Two numbers are in the ratio 2 : 3. If 2 is subtracted from the first and 2 is added to the second, the ratio becomes 1 : 2. The sum of the numbers is :

(1) 30

(2) 28

(3) 24

(4) 10

10.The ratio of incomes of two persons is 5 : 3 and that of their expenditures is 9 : 5. If they save Rs, 2600 and Rs. 1800 respectively, their incomes are :

(1) Rs. 8000; Rs. 4800

(2) Rs. 6000; Rs. 3600

(3) Rs. 10000; Rs. 6000

(4) Rs. 9000; Rs. 5400

Answers and Solution:

1. (2)

Number = 269*68

= 269 * (67+1)

= 269 * 67 + 269

clearly,remainder is obtained on dividing 269 by 67 that is 1.

2. (4)

Let x+y = 20 and x-y = 8

S0 (x+y)(x-y) = 20*8

=> x^2-y^2 = 160

3. (2)

Here x*y = 3x+2y

so 2*3+3*4 = (3*2+2*3)+(3*3+2*4)

= 12+17=29

4. (1)

Let the number of students be x.then,

=> 7 = (x*6+12*40)/(x+12)

=7x + 84 = 6x + 480

=> x = 396

5. (2)

6. (3)

10% of A = 15% 0f B = 20* 0f C

=> 10A = 15B = 20C

=> 10A/60 = 15B/60 = 20C/60

=> A/6 = B/4 = C/3

So A : B : C = 6 : 4 : 3

so 6x + 4x + 3x = 7800

=> 13x = 7800

x = 600

B's income = 4x = 600*4 = 2400

7.(2)

8. (4)

9. (1)

10. (1)

Let the incomes of two persons be Rs.5x and 3x rupess and their expenditure be Rs.9x and 5x respectively,

As given

5x - 9y = 2600.......(1)

3x - 5y = 1800.......(2)

by solve

then, x = 1600

So First person's income = 1600*5 = 8000

Second's person income = 1600*3 = 4800

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

### Set B

1. 8% of the votes 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:

(1). 21000

(2). 23500

(3). 22000

(4). 27500

2. Three numbers which are co-prime to one another are such that the product of the first two is 551 and that of the last two is 1073.The sum of the three numbers is :

(1). 75

(2). 81

(3). 85

(4). 89

3. A number of boys raised Rs.400 for a famine relief fund,each boy giving as many 25 paise coins as there were boys.The number of boys was:

(1). 40

(2). 16

(3). 20

(4). 100

4. The difference between simple interest and compound interest compounded annually,on a certain sum of money for two years at 4% per annum is Rs.1 The sum (in Rs.) is:

(1). 650

(2). 630

(3). 625

(4). 640

5. What sum of money will amount to Rs. 520 in 5 years and to Rs.568 in 7 years at simple interest ?

(1). Rs.400

(2). Rs.120

(3). Rs.510

(4). Rs.220

6. If 72 men can build a wall of 280 m length in 21 days ,how many men could take 18 days to build a similar type of wall of length 100 m?

(1). 30

(2). 10

(3). 18

(4). 28

7. Babu and Asha can do a job together in 7 days .Asha is 1(3/4) times as efficient as Babu.The same job can be done by Asha alone in

(1). 49/4 days

(2). 49/3 days

(3). 11 days

(4). 28/3 days

8. Two pipes A and B can separately fill a cistern in 60 minutes and 75 minutes respectively.There is a third pipe in the bottom of the cistern to empty it.If all the there pipes are simultaneously opened, then the cistern is full in 50 minutes.In how much time the third pipe alone can empty the cistern?

(1). 110 minutes

(2). 100 minutes

(3). 120 minutes

(4). 90 minutes

9. The difference between two positive numbers is 3. If the sum of their square is 369,then the sum of the numbers is:

(1). 81

(2). 33

(3). 27

(4). 25

10. Let the least number of six digits which when divided by 4,6,10,15 leaves in each case same remainder 2 be N. The sum of digits in N is:

(1). 3

(2). 5

(3). 4

(4). 6

Answers and Solution:

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

Number of uncast votes = 8

so Number of votes polled = 92

Number of votes obtained by winner = 48

so 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,

So Total votes = 100/4*1100 = 27500

2.(3)

Let the numbers be x,y and Z which are prime to one another .

Now,xy = 551

yz = 1073

so y = HCF of 551 and 1073

so y = 29

so x = 551/29 = 19

and z = 1073/29 = 37

So sum = 19+29+37 = 85

3.(1)

4.(3)

The difference between compound interest and simple interest for two years

= p*(R)^2/(100*100)

so 1 = p*(4)^2/(100*100)

=> p = 625

5.(1)

6.(1)

We know that

W1/M1D1 = w2/M2D2

where x = no of man

=> 280/(72*21) = 100/(x*18)

x = 30

7.(3)

8.(2)

Let the third pipe empty the cistern in x minutes.

part of cistern filled in 1 minute when all three pipers are opened simultaneously

= 1/60 + 1/75 - 1/x

According to question

=> 1/60 + 1/75 - 1/x = 1/50

x = 100 minutes

9.(3)

10.(2)

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