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

### Set A

1. A shopkeeper announces successive discounts of 10% and 20%. Find the equivalent percent discount.

A. 27%

B. 28%

C. 29%

D. 30%

2. In a college, 40% of the students were allotted group A, 75% of the remaining were given group B and the remaining 12 students were given group C. Then the number of students who applied for the groups is:

A. 80

B. 92

C. 100

D. 60

3.Two students appeared at an examination. One of them secured 9 marks more than the other and his marks was 56% of the sum of their marks. The marks obtained by them are:

A. 39, 30

B. 41, 32

C. 42, 33

D.43, 34

4. In a competitive examination in State A, 6% candidates got selected from the total appeared candidates. State B had an equal number of candidates appeared and 7% candidates got selected with 80 more candidates got selected than A. What was the number of candidates appeared from each State?

A. 8200

B. 7500

C. 7000

D. 8000

5. The price of a car is Rs. 3,25,000. It was insured to 85% of its price. The car was damaged completely in an accident and the insurance company paid 90% of the insurance. What was the difference between the price of the car and the amount received ?

A. Rs. 76,375

B. Rs. 34,000

C. Rs. 82,150

D. Rs. 70,000

6. Gauri went to the stationers and bought things worth Rs. 25, out of which 30 paise went on sales tax on taxable purchases. If the tax rate was 6%, then what was the cost of the tax free items?

A. Rs. 15

B. Rs. 15.70

C. Rs. 19.70

D. Rs. 20

7. In a certain school, 20% of students are below 8 years of age. The number of students above 8 years of age is of the number of students of 8 years of age which is 48. What is the total number of students in the school?

A. 72

B. 80

C. 120

D. 100

8. A’s salary is 30% higher than B’s salary. The percent that B’s salary is less than A’s salary is:

A. 25%

B. 30%

C. 23 1/13%

D. 20%

9. If the price of sugar is increased by 25%, by how much percent must a householder reduce his consumption of sugar so as not to increase his expenditure on sugar?

A. 35%

B. 30%

C. 25%

D. 20%

10. In a class of 40 students and 8 teachers, each student got sweets that are 20% of the total number of students and each teacher got sweets that are 25% of the total number of students. How many sweets were there?

A. 420

B. 400

C. 320

D. 360

Answer and Solution :

1(B)Explanation

For two successive changes of x% and y%, net change =

{x + y +xy/100}%

= {-10-20+(-10)(-20)/100}%

=(-30 + 2) %

= – 28%

2(A)Explanation

Let the number of students be 100.

Number of students allotted to group A = 40

Number of students allotted to group B = 75% of 60 = 45

Thus, Balance number of students allotted to group C = 100 – 40 – 45 = 5

Number of actual students = 100/15 * 12 = 80

3(C)Explanation:

Let their marks be (x + 9) and x.

Then, x + 9 = 56/100(x + 9 + x)

=>25(x + 9) = 14(2x + 9)

=>3x = 99

=>x =33

So, their marks are 42 and 33.

4(D)Explanation :

State A and State B had an equal number of candidates appeared.

In state A, 6% candidates got selected from the total appeared candidates

In state B, 7% candidates got selected from the total appeared candidates

But in State B, 80 more candidates got selected than State A

From these, it is clear that 1% of the total appeared candidates in State B = 80

=> total appeared candidates in State B = 80 x 100 = 8000

=> total appeared candidates in State A = total appeared candidates in State B = 8000

5(A)Explanation :

Price of the car = Rs.3,25,000

Car insured to 85% of its price

=>Insured price=325000×85/100

Insurance company paid 90% of the insurance

Amount paid by Insurance company =Insured price×90/100

=325000×85/100×90/100=325×85×9=Rs.248625

Difference between the price of the car and the amount received

= Rs.325000 – Rs.248625 = Rs.76375

6(C)Explanation:

Let the amount taxable purchases be Rs. x.

Then, 6% of x = 30/100

=> x = (30/100 x 100/6) = 5

so Cost of tax free items = Rs. [25 – (5 + 0.30)] = Rs. 19.70

7(D)Explanation:

Let the number of students be x. Then,

Number of students above 8 years of age = (100 – 20)% of x = 80% of x.

so 80% of x = 48 + 2/3 of 48

=> 80/100 x = 80

=> x = 100.

8(C)Explanation:

Let B’s salary be Rs. 100

Then , A’s salary = Rs.130

Required percentage = 30/100 * 100 = 23 1/13%

9(D) Explanation:

If the price of a commdity increases by R% , then the reduction in consumption so as not to increase the expenditure is :

{(R/(100+R)x100}%

Thus, percent reduction in consumption = {(25/(100+25)x100}%

= 20 %

10(B)Explanation :

Number of students in the class = 40

Sweets received by 40 students = 40 * (20% of 40) = 320

Number of teachers in the class = 8

Sweets received by 8 teacher = 8 * (25% of 40) = 80

Total number of sweets = 320 + 80 = 400

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

### Set B

1.Father is aged three times more than his son Sunil. After 8 years, he would be two and a half times of Sunil’s age. After further 8 years, how many times would he be of Sunil’s age?

A. 4 times

B. 4 times

C. 2 times

D. 3 times

2. The sum of ages of 5 children born at the intervals of 3 years each is 50 years. What is the age of the youngest child?

A. 4 years

B. 8 years

C. 10 years

D. None of these

3.A man’s age is 125% of what it was 10 years ago, but 83 1/3 % of what it will be after ten 10 years. What is his present age?

A. 70

B. 60

C. 50

D. 40

4. A father said to his son, “I was as old as you are at the present at the time of your birth”. If the father’s age is 38 years now, the son’s age five years back was:

A. 14 years

B. 19 years

C. 33 years

D. 38 years

5. Present ages of Kiran and Syam are in the ratio of 5 : 4 respectively. Three years hence, the ratio of their ages will become 11 : 9 spectively. What is Syam’s present age in years?

A. 28

B. 27

C. 26

D. 24

6. Six years ago, the ratio of the ages of Kunal and Sagar was 6 : 5. Four years hence, the ratio of their ages will be 11 : 10. What is Sagar’s age at present?

A. 16 years

B. 18 years

C. 20 years

D. Cannot be determined

7. The Average age of a class of 22 students is 21 years. The average increased by 1 when the teacher’s age also included. What is the age of the teacher?

A. 48

B. 45

C. 43

D. 44

8.My brother is 3 years elder to me. My father was 28 years of age when my sister was born while my mother was 26 years of age when I was born. If my sister was 4 years of age when my brother was born, then what was the age my father when my brother was born?

A. 35 years

B. 34 years

C. 33 years

D. 32 years

9. The present ages of three persons in proportions 4 : 7 : 9. Eight years ago, the sum of their ages was 56. Find their present ages (in years).

A. 8, 20, 28

B. 16, 28, 36

C. 20, 35, 45

D. None of these

10.The ages of two persons differ by 16 years. 6 years ago, the elder one was 3 times as old as the younger one. What are their present ages of the elder person?

A. 10

B. 20

C. 30

D. 40

ANSWERS AND SOLUTION :

1(C)Explanation :

Assume that Sunil’s present age = x.

Then father’s present age = 3x + x = 4x

After 8 years, fathers age = 2 ½ times of Sunils’ age

=> (4x+8) = 2 ½ × (x+8)

=> 4x + 8 = (5/2) ×(x + 8)

=> 8x + 16 = 5x+ 40

=> 3x = 40-16 = 24

=> x = 24/3 = 8

After further 8 years,

Sunil’s age = x + 8+ 8 = 8+8+8 = 24

Father’s age = 4x + 8 + 8 = 4 × 8 + 8 + 8 = 48

Father’s age/Sunil’s age = 48/24 = 2

2(A)Explanation:

Let the ages of children be x, (x + 3), (x + 6), (x + 9) and (x + 12) years.

Then, x + (x + 3) + (x + 6) + (x + 9) + (x + 12) = 50

=> 5x = 20

=> x = 4.

So Age of the youngest child = x = 4 years.

3(C)Explanation :

Let the age before 10 years = x

Then 125x/100 = x + 10

=>125x = 100x + 1000

=> x = 1000/25 = 40

Present age = x + 10 = 40 +10 = 50

4(A)Explanation:

Let the son’s present age be x years. Then, (38 – x) = x

=>2x = 38.

=> x = 19.

So Son’s age 5 years back (19 – 5) = 14 years.

5(D)Explanation :

Ratio of the present age of Kiran and Syam = 5 : 4

=> Let the present age of Kiran = 5x

Present age of Syam = 4x

After 3 years, ratio of their ages = 11:9

=> (5x + 3) : (4x + 3) = 11 : 9

=> (5x+3) / (4x+3) = 11/9

=> 9(5x + 3) = 11(4x + 3)

=> 45x + 27 = 44x + 33

=> x = 33-27 =6

Syam’s present age = 4x = 4×6 = 24

6(A)Explanation:

Let the ages of Kunal and Sagar 6 years ago be 6x and 5x years respectively.

Then, ((6x + 6) + 4)/(5x + 6) + 4 = 11/10

=> 10(6x + 10) = 11(5x + 10)

=> 5x = 10

=> x = 2.

So Sagar’s present age = (5x + 6) = 16 years.

7(D)Explanation :

Total age of all students = 22×21

Total age of all students + age of the teacher = 23 × 22

Age of the teacher = 23×22 – 22×21 = 22(23-21) = 22×2 = 44

8(D)Explanation :

Let my age = x

Then

My brother’s age = x + 3

My mother’s age = x + 26

My sister’s age = (x + 3) + 4 = x + 7

My Father’s age = (x + 7) + 28 = x + 35

=> age my father when my brother was born = x + 35 – (x + 3) = 32

9(B)Explanation:

Let their present ages be 4x, 7x and 9x years respectively.

Then, (4x – 8) + (7x – 8) + (9x – 8) = 56

=> 20x = 80

=> x = 4.

So Their present ages are 4x = 16 years, 7x = 28 years and 9x = 36 years respectively.

10(C)Explanation :

Let’s take the present age of the elder person = x

and the present age of the younger person = x – 16

(x – 6) = 3 (x-16-6)

=> x – 6 = 3x – 66

=> 2x = 60

=> x = 60/2 = 30

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

### Set C

1. A wire is in the form of a circle . The radius of the circle is 28 cm. The wire is then moulded to form a square . find the side of the square formed?

A. 44 cm

B. 66 cm

C. 22 cm

D. 11 cm

2. A sum of Rs. 2500 amounts to Rs. 3875 in 4 years at the rate of simple interest. What is the rate of interest?

A. 12.25%

B. 12%

C. 6%

D. 13.75%

3. What will be the day of the week 15th August, 2010?

A. Sunday

B. Monday

C.Tuesday

D. Friday

4. A, B, C subscribe Rs. 50,000 for a business. A subscribes Rs. 4000 more than B and B Rs. 5000 more than C. Out of a total profit of Rs. 35,000, A receives:

A. Rs. 8400

B. Rs. 11,900

C. Rs. 13,600

D. Rs. 14,700

5. 40 men can make 60 toys in 8 hours. if 8 men leave the work then how many toys can be made in 12 hours?

A. 56

B. 60

C. 66

D. 72

6. Running at the same constant rate, 6 identical machines can produce a total of 270 bottles per minute. At this rate, how many bottles could 10 such machines produce in 4 minutes?

A. 648

B. 1800

C. 2700

D. 10800

7. How much percent more than the cost price should a shopkeeper mark his goods so that after allowing a discount of 25% on the marked price , he gain 20% ?

A. 60%

B. 55%

C. 70%

D. 50%

8. The L.C.M. of two numbers is 48. The numbers are in the ratio 2 : 3. Then sum of the number is:

A. 28

B. 32

C. 40

D. 64

9. A train has a length of 150 meters . it is passing a man who is moving at 2 km/hr in the same direction of the train, in 3 seconds. Find out the speed of the train.

A. 182 km/hr

B. 180 km/hr

C. 152 km/hr

D. 169 km/hr

10. In a 100 m race, A beats B by 10 m and C by 13 m. In a race of 180 m, B will beat C by:

A. 5.4 m

B. 4.5 m

C. 5 m

D. 6 m

ANSWERS AND SOLUTION:

1(A)Explanation :

Radius of the circle (r) = 28 cm.

Length of the wire (circumference) = 2 pi r = 2 pi 28 = 176 cm

Let side of the square be “a” cm.

Perimeter of square(4a) = Circumference of the circle = 176 cm

or, 4a = 176 cm

or, a = 44 cm

Thus, side of the square is 44 cm.

2(D)Explanation :

Simple Interest, SI = (3875 – 2500) = Rs.1375

Principal, P = Rs. 2500

Time, T = 4 years

R = ?

R = (100×SI)/PT= (100×1375)/2500×4 = 100×1375/10000=13.75%

3(A)Explanation:

15th August, 2010 = (2009 years + Period 1.1.2010 to 15.8.2010)

Odd days in 1600 years = 0

Odd days in 400 years = 0

9 years = (2 leap years + 7 ordinary years) = (2 x 2 + 7 x 1) = 11 odd days 4 odd days.

Jan. Feb. March April May June July Aug.

(31 + 28 + 31 + 30 + 31 + 30 + 31 + 15) = 227 days

So 227 days = (32 weeks + 3 days) 3 odd days.

Total number of odd days = (0 + 0 + 4 + 3) = 7 = 0 odd days.

Given day is Sunday.

4(D)Explanation:

Let C = x.

Then, B = x + 5000 and A = x + 5000 + 4000 = x + 9000.

So, x + x + 5000 + x + 9000 = 50000

=> 3x = 36000

=> x = 12000

A : B : C = 21000 : 17000 : 12000 = 21 : 17 : 12.

A’s share = Rs.(35000 x 21/50) = Rs. 14,700.

5(D)Explanation:

Here M1 = 40, T1 = 8 hours, W1 = 60 and M2 = 32, T2 = 12, W2 = ?

M1 x T1 x W2 = M2 x T2 x W1

So 40 x 8 x W2 = 32 x 12 x 60

or, W2 = 23040/320 = 72

6(B)Explanation:

Let the required number of bottles be x.

More machines, More bottles (Direct Proportion)

More minutes, More bottles (Direct Proportion)

Machines 6 : 10

:: 270 : x

Time (in minutes) 1 : 4

So 6 x 1 x x = 10 x 4 x 270

x = (10 x 4 x 270)/(6)

x = 1800.

7(A)Explanation:

Let cost price of goods be Rs 100.

Gain = 20%

Therefore, selling price = Rs 120

Discount = 25%

Marked Price = (100/(100 – 25) x 120)

= Rs. 160

i .e. 60% more

8(C)Explanation:

Let the numbers be 2x and 3x.

Then, their L.C.M. = 6x.

So, 6x = 48 or x = 8.

So, The numbers are 16 and 24.

Hence, required sum = (16 + 24) = 40.

9(A)Explanation :

Length of the train, l = 150m

Speed of the man , Vm= 2 km/hr

Relative speed, Vr = total distance/time = (150/3) m/s = (150/3) × (18/5) = 180 km/hr

Relative Speed = Speed of train, Vt – Speed of man (As both are moving in the same direction)

=> 180 = Vt – 2

=> Vt = 180 + 2 = 182 km/hr

10(D)Explanation:

A : B = 100 : 90.

A : C = 100 : 87.

B/C = B/A x A/C = 90/100 x 100/87 = 30/29 .

When B runs 30 m, C runs 29 m.

When B runs 180 m, C runs (29/30 x 180) m = 174 m.

B beats C by (180 – 174) m = 6 m.