EduSahara™ Worksheet

Question 1

1.

The sum of the squares of two consecutive odd numbers is 202. Find the numbers

(i)
(-11)

,

(-9)

or

11

,

9
(ii)
(-10)

,

(-8)

or

10

,

8
(iii)
(-13)

,

(-12)

or

13

,

12
(iv)
(-8)

,

(-7)

or

8

,

7
(v)
(-12)

,

(-10)

or

12

,

10

Question 2

2.

Find two natural numbers which differ by 17 and the sum of whose squares is 985

(i)

(

10

,

27

)
(ii)

(

11

,

28

)
(iii)

(

14

,

32

)
(iv)

(

13

,

30

)
(v)

(

12

,

29

)

Question 3

3.

The sum of the squares of two consecutive even numbers is 244. Find the numbers

(i)
11

,

13

or

(-11)

,

(-13)
(ii)
10

,

12

or

(-10)

,

(-12)
(iii)
9

,

11

or

(-9)

,

(-11)
(iv)
8

,

9

or

(-8)

,

(-9)
(v)
13

,

15

or

(-13)

,

(-15)

Question 4

4.

One pipe can fill a cistern in
2
hours less than the other.

The two pipes together can fill it in
6

6
13
hrs.

Find the time that each pipe will take to fill the cistern.

(i)

12 hr , 14 hr
(ii)

11 hr , 13 hr
(iii)

9 hr , 11 hr
(iv)

13 hr , 15 hr
(v)

14 hr , 17 hr

Question 5

5.

In a two digit number, the unit's digit exceeds it ten's digit by 4 and the product of the given number and the sum of its digits is equal to 370 . Find the number

(i)

59
(ii)

48
(iii)

26
(iv)

15
(v)

37

Question 6

6.

The denominator of a fraction exceeds the numerator by
3
.

The square of the fraction is equal to
169
256
. Find the fraction

(i)

13
14
(ii)

11
16
(iii)

13
18
(iv)

13
16
(v)

15
16

Question 7

7.

In a two digit number, the unit's digit exceeds it ten's digit by 1 and the product of the given number and the sum of its digits is equal to 1513 . Find the number

(i)

78
(ii)

111
(iii)

100
(iv)

89
(v)

67

Question 8

8.

Three consecutive natural numbers are such that the square of the middle number exceeds the difference of the squares of the other two by 221 . Find the three numbers.

(i)

16, 17, 18
(ii)

13, 14, 15
(iii)

15, 16, 17
(iv)

17, 18, 19
(v)

18, 19, 20

Question 9

9.

The sum of the numerator and denominator of a fraction is
8
.

If
5
is added to both the numerator and denominator,

the fraction is increased by
1
5
. Find the fraction

(i)

1
(ii)

3
5
(iii)

1
5
(iv)

5
3

Question 10

10.

A number is of two digits. The digit in unit's place is the square of the digit in ten's place. The number formed by reversing the digits exceeds twice the number by (-6) . Find the number

(i)

27
(ii)

24
(iii)

25
(iv)

21
(v)

23

Question 11

11.

A two digit number is such that the product of the digits is 8. When 18 is subtracted from the number, the digits are reversed. Find the number

(i)

42
(ii)

43
(iii)

44
(iv)

41
(v)

40

Question 12

12.

A play field is
40.00 m
by
30.00 m
.
It has a road all around it on the outside.

Find the width of the road if its area is
17
16
of the area of the play field

(i)

5.50 m
(ii)

6.50 m
(iii)

9.50 m
(iv)

8.50 m
(v)

7.50 m

Question 13

13.

The sum of the squares of two consecutive even numbers is 164. Find the numbers

(i)
(-11)

,

(-9)

or

11

,

9
(ii)
(-13)

,

(-11)

or

13

,

11
(iii)
(-7)

,

(-5)

or

7

,

5
(iv)
(-9)

,

(-7)

or

9

,

7
(v)
(-10)

,

(-8)

or

10

,

8

Question 14

14.

A stream flows from A to B, a distance of 12.00 km. A man who can row in still water at 10.00 kmph, can row up and down in 4.71 hr . What is the speed of the stream?

(i)

5.00 kmph
(ii)

9.00 kmph
(iii)

6.00 kmph
(iv)

7.00 kmph
(v)

8.00 kmph

Question 15

15.

The sum of the numerator and denominator of a fraction is
24
.

If
5
is added to both the numerator and denominator,

the fraction is increased by
5
42
. Find the fraction

(i)

16
8
(ii)

4
7
(iii)

3
8
(iv)

5
8
(v)

8
16

Question 16

16.

51 is divided into two parts such that the sum of their reciprocals is
51
344
.

Find the two parts

(i)

(

6

,

45

)
(ii)

(

8

,

43

)
(iii)

(

10

,

41

)
(iv)

(

7

,

44

)
(v)

(

9

,

42

)

Question 17

17.

Twice the square of a number exceeds 3 times the number by 189. Find the number

(i)

(-12)
(ii)

(-6)
(iii)

(-10)
(iv)

(-8)
(v)

(-9)

Question 18

18.

The area of a rectangular room is 480.00 sq.m. If the length and breadth are increased by 7 m, the area would become 893.00 sq.m. Find the original dimensions of the room

(i)

12.00 m , 40.00 m
(ii)

3.00 m , 160.00 m
(iii)

2.00 m , 240.00 m
(iv)

4.00 m , 120.00 m

Question 19

19.

Find the number which is less than its square by 210

(i)

14
(ii)

18
(iii)

16
(iv)

13
(v)

15

Question 20

20.

Find the number which exceeds its reciprocal by
0

(i)

0
(ii)

2
(iii)

1
(iv)

-1
(v)

3

Question 21

21.

The product of two consecutive numbers is 56. Find the numbers

(i)

-8 , -7 or 8,7
(ii)

-7 , -6 or 7 , 6
(iii)

-11 , -9 or 11 , 9
(iv)

-9 , -8 or 9 , 8
(v)

-5 , -5 or 5 , 5

Question 22

22.

The sum of the ages of a father and his son is 36 years whereas three years ago, the product of their ages was 81. Find the current ages of the son and the father.

(i)

6 years , 30 years
(ii)

7 years , 29 years
(iii)

4 years , 32 years
(iv)

5 years , 31 years
(v)

8 years , 28 years

Question 23

23.

If the difference of two numbers is 9 and their product is 580, find the numbers

(i)
(-20)

,

(-29)

or

20

,

29
(ii)
(-21)

,

(-30)

or

21

,

30
(iii)
(-23)

,

(-31)

or

23

,

31
(iv)
(-19)

,

(-28)

or

19

,

28
(v)
(-18)

,

(-26)

or

18

,

26

Question 24

24.

A can do a work in
x
days and B can do it in
(

x

+

11

)
days.

Both of them working together can do it in
13

41
57
days. Calculate
x

(i)

21
(ii)

24
(iii)

22
(iv)

25
(v)

23

Question 25

25.

The perimeter of a rectangular room is 82.00 m and the length of its diagonal is 32.57 m . Find the dimensions of the room

(i)

29.00 m , 12.00 m
(ii)

31.00 m , 10.00 m
(iii)

30.00 m , 11.00 m
(iv)

32.00 m , 9.00 m
(v)

33.00 m , 8.00 m

Assignment Key