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

### Set A

1.Rs.6,000 becomes Rs. 6,720 in a year at SI. What will Rs. 9,600 become at the end of three years at the same rate of simple interest?

(a) Rs. 13,056

(b) Rs. 14, 048

(c) Rs. 15, 024

(d) Rs. 16, 014

2.The number nearest to 27987 which is divisible by 43 is .

(a) 27950

(b) 27962

(c) 27981

(d) 27993

3.Two metallic cylinders of heights 5 cm and 4 cm and both having the same base radii of 2 cm are melted to form a sphere. Find the radius of the sphere.

(a) 2 cm

(b) 3 cm

(c) 4 cm

(d) 5 cm

4.If a^4 – b^4 = 65 and a – b = 1, where a and b are positive integers, then the value of (a^2 + b^2) is _________ .

(a) 13

(b) 15

(c) 17

(d) 19

5.A Shopkeeper offered a discount of 15% on a certain product and gained a profit of 20%. If the marked price is Rs. 13800, then what is the profit earned by the shopkeeper?

(a) Rs. 1215

(b) Rs. 1505

(c) Rs. 1955

(d) Rs. 2405

6.If (4x^2 + 7y^2) : 2 x y = 16 : 3 then the value of (x + y)/(x – y) which is not a multiple of 5 is _

(a) 7

(b) 11

(c) 13

(d) None of these.

7.The monthly salary of Kishore is Rs. 15, 000. His salary is increase by 8%. His expenditure is increased by Rs. 720 which is 6% of the previous expenditure. The savings of Kishore after the increase is __________.

(a) Rs. 3, 240

(b) Rs. 3, 480

(c) Rs. 3, 600

(d) Rs. 3, 720

8.Find the next number of the following series.

9, 10, 19, 44, 93, __________

(a) 174

(b 180

(c) 186

(d) 192

9.A shopkeeper gave a discount of Rs. 30 on a product such that the discount percentage is same as the profit percentage. If the cost price of the product is Rs. 100, find the selling price of the product.

(a) Rs.112

(b) Rs. 150

(c) Rs. 130

(d) Rs. 120

10.A vegetable vendor bought 10 kg of tomatoes for Rs. 100 and sold them at a rate of 8 kg for Rs. 120. The profit percentage of the vendor is ________.

(a) 20%

(b) 25%

(c) 40%

(d) 50%

ANSWERS AND SOLUTION:

1(a)Let’r” be the rate of intrest.

=>6000(1+r/100)= 6700

=>1+r/100= 6720/6000

=>1 + r/100 = 1.12

=>r/100=1.12-1= 0.12

r=(100)(.12)=12%

so 9600 in three years

=9600(1+(3×12)/100)

=9600(1.36)=Rs.13056

2(d)we have

27987 = 43(650) + 37

and 27987=43(651)-6

so 27993 is nearest to 27987 and is divisibleby 43

3(b)

Let “r” be the radius of the sphere,

The total volume of the two cylinder is equal to volume of the sphere formed.

=>π r1^2 h1^2 + π r2^2 h2=4/3πr3^3

=>4/3πr^3 = π(2)^2×5+π(2)^2×4

=>4/3r^3 = 20+16

=4/3r^3 =36

=>r^3 = 9×3=27

r=3

so The radius of the sphere formed is 3cm.

4(a)

Given that,a^4-b^4=65

a-b=1

a^4-b^4=(a^2-b^2)(a^2+b^2)

=(a-b)(a+b)(a^2+b^2)

=(a+b)(a^2+b^2)=65

we have

65=1×65 or 5×13

=>(a+b)(a^2+b^2)5×13

(a and b are positive integers,a-b=1 and a+b>1)

=a+b =5, a^2+b^2=12

a=2;b=3 or a=3,b=2

so a^2+b^2=13.

5(c) From the given data, SP = 85% of M.P

From the given data,SP= 85%of M.P

=85/100×13800=Rs.(85×138)

we know,profit = SP-CP

=SP-100/120SP = SP(1-100/120)

=85x138x20/120 = Rs.1955

6(c)

Given that

(4x^2+7y^2):2xy=16:3

=>3(4x^2 + 7y^2)=16 X 2xy

=>12x^2 + 21y^2 = 32xy

=>12x^2-32xy+21y^2=0

=>(6x-7y)(2x-3y) = 0

=>x/y=7/6 or 3/2

for x/y=7/6,(x+y)/(x-y) = (7+6)/(7-6)=13

for x/y=3/2,(x+y)/(x-y) = (3+2)/(3-2)=5

But (x+y)/(x-y)is not a multiple of 5=>(x+y)/(x-y)=13

7(b)

8(a)

9(d)

10(d)

The cost price of 1kg of tomatoes=100/10=10

The selling price of 1kg of tomatoes= 120/8=15

so The profit percentage obtained by him=(15-10)/10×100 =50%

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

### Set B

1.If the sum of two numbers be multiplied by each number separately, the products so obtained are 247 and 114. The sum of the numbers is

(a) 19

(b) 20

(c) 21

(d) 23

2.Find a number, one-seventh of which exceeds its eleventh part by 100.

(a) 1925

(b) 1825

(c) 1540

(d) 1340

3.A can do a work in 12 days. When he had worked for 3 days, B joined him. If they complete the work in 3 more days, in how many days can B alone finish the work?

(a) 6 days

(b) 12 days

(c) 4 days

(d) 8 days

4.A and B can complete a piece of work in 8 days, B and C can do it in 12 days, C and A can do it in 8 days. A, B and C together can complete it in

(a) 4 days

(b) 5 days

(c) 6 days

(d) 7 days

5.The volume (in m^3) of rain water that can be collected from 1.5 hectares of ground in a rainfall of 5 cm is

(a) 75

(b) 750

(c) 7500

(d) 75000

6.The perimeter of a triangle is 40cm and its area is 60 cm^2. If the largest side measures 17 cm, then the length (in cm) of the smallest side of the triangle is

(a) 4

(b) 6

(c) 8

(d) 15

7.What single discount is equivalent to two successive discounts of 20% and 15% ?

(a) 35%

(b) 32%

(c) 34%

(d) 30%

8.What number should be added to or subtracted from each term of the ratio 17 : 24 so that it becomes equal to 1 : 2?

(a) 5 is subtracted

(b) 10 is added

(c) 7 is added

(d) 10 is subtracted

9.If the selling price of 10 articles is equal to the cost price of 11 articles, then the gain percent is

(a) 10

(b) 11

(c) 15

(d) 25

10.If 90% of A = 30% of B and B = 2x% of A, then the value of x is

(a) 450

(b) 400

(c) 300

(d) 150

ANSWERS AND SOLUTION:

1(A)Let the number be x and y

x(x+y)=247

and y(x+y)=114

=>x^2+xy=247 and xy+y^2=114

On adding

=>x^2+xy+xy+y^2=247+14

=>x^2+2xy+y^2=361

=>(x+y)^2=19^2=>x+y=19

2(A)

Let the number be x.

x/7-x/11 = 100

=>(11x-7x)/(11×7)=100

=> 4x = 77 x 100

=> x = 1925

3(A)

Let be alone do the work in x days.

6 x 1/12+3×1/x =1

=>1/2+3/x =1

=>3/x= 1/2=>x = 6 days

4(C)

(A+B)’s 1day’s work=1/8

(B+C)’s 1day’s work=1/12

(C+A)’s 1 day’s work 1/8

On adding

2(A+B+C)’s 1day’s work

=1/8+1/12+1/8=(3+2+3)/24

=8/24=1/3

so (A+B+C)’s 1day’s work = 1/6

Hence,the work will be completed in 6days.

5(B)

1 hectare = 10000sq.m

Area of the ground =15000sq.m

so Required volume=15000×5/100=750cubic meter

6(C)

7(B)

Single equivalent discount =(x+y-xy/100)%

=(20+15-(20 x 15)/100)%=32%

8(D)

Let the number be x be added

(17+x)/(24+x)=1/2

=>34 + 2x = 24+x

=>2x-x = 24-34

=-10

Hence, 10 should be subtracted.

9(A)

10(D)

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

### Set C

1.The LCM of two multiples of 12 is 1056. If one of the numbers is 132, the other number is

(1) 12

(2) 72

(3) 96

(4) 132

2.A number when divided by 192 gives a remainder of 54. What remainder would be obtained on dividing the same number by 16?

(1) 2

(2) 4

(c) 6

(4) 8

3.Jyothi can do 3/4th of a job in 12 days. Mala is twice as efficient as Jyothi. In how many days will Mala finish the job?

(1) 6

(2) 8

(3) 12

(4) 16

4.A is twice as good a workman as B and B is twice as good a workman as C. If A and B can together finish a piece of work in 4 days, then C can do it by himself in

(1) 6 days

(2) 8 days

(3) 24 days

(4) 12 days

5.Two solid cylinders of radii 4 cm and 5 cm and lengths 6 cm and 4 cm respectively are recast into cylindrical disc of thickness 1 cm. The radius of the disc is

(1) 7 cm

(2) 14 cm

(3) 21 cm

(4) 28 cm

6.A road of 5 km length will be constructed in 100 days. So 280 workers were employed. But after 80 days it was found that only 3½ km road was completed. Now how many more people were needed to finish the work in the specified time?

(1) 480

(2) 80

(3) 200

(4) 100

7.A constant distance from Chennai to Bangalore is covered by Express train at 100 km/hr. If it returns to the same distance at 80 km/hr, then the average speed during the whole journey is

(1)90.20 km/hr

(2)88.78 km/hr

(3)88.98 km/hr

(4)88.89 km/hr

8.The average weight of 15 students in a class increases by 1.5kg when one of the students weighing 40 kg is replaced by a new student. What is the weight (in kg) of the new student?

(1) 64.5

(2) 56

(3) 60

(4) 62.5

9.By selling a basket for Rs. 19.50, a shopkeeper gains 30%. For how much should he sell it to gain 40% ?

(1) Rs. 21

(2) 21.50

(3) Rs. 24

(4) Rs. 23

10.A person sold a TV for Rs. 9,400 and he sold a particular amount. When he sold another TV of the same type at Rs. 10,600, his gain was double the former loss. What was the cost price of each TV?

(1) Rs. 9, 800

(2) Rs. 10,000

(3) Rs. 10, 200

(4) Rs. 10, 400

ANSWERS AND SOLUTION:

1(3) Let the numbers be 12x and 12y.

Their LCM = 12xy when x and y are prime to each other.

so Y = 1056/132 = 8 [12x = 132]

Other number = 12y

= 12 * 8 = 96

2(3) Here, the first divisor 192 is a multiple of second divisor 16.

so Required remainder

= remainder obtained by dividing 54 by 16 = 6

3(2) Jyothi can do 3/4 th of a job in 12 days.

Jyothi can do 1 job in (12 *4)/3 = 16 days.

As Mala is twice as efficient as Jyothi.

so Mala will finish the job in 8 days.

4(3) According to the question,

If A takes x days to complete the work, B will take 2x days and C will take 4x days,

Now, (A + B)’s 1 day’s work

= 1/4

= 1/x + 1/2x= 1/4

= (2+1)/2x = 1/4

2x = 12

X = 6

C will complete the work in 24 days.

5(2) Sum of the volumes of two cylinders

= πr1^2 h1+ πr2^2 h2

= 22/7 (4 * 4 * 6 + 5 * 5 * 4)

= 22/7 (96 + 100)

= 22/7 * 196 = 616 cm3

Let the radius of the disc be r cm.

so πr^2*1=616

= 22/7 * r^2 = 616

= r^2 = (616 * 7)/22 = 196

r = √196 = 14 cm

6(3)

7(4)

If same distances are covered at two different speeds of x and y kmph,the average speed of journey=2xy/x+y

=(2x100x80)/(100+80)

=88.89

8(4)

9(1)

Let CP of basket be Rs.y.

13% of y = 19.5

=(130 x y)/100 = 19.5

=>y= (19.5 x 100)/130=Rs.15

For 40% gain

SP = (140×15)/100=21

10(1)

Let CP of each TV be Rs.x

According to the question,

2(x-9400)=10600-x

=>2x-18800=10600-x

=>3x = 10600+18800

=29400

=>x = 29400/3= Rs.9800