EduSahara™ Worksheet

Question 1

1.

The denominator of a fraction exceeds the numerator by
3
.

The square of the fraction is equal to
4
9
. Find the fraction

(i)

6
11
(ii)

8
9
(iii)

6
7
(iv)

2
3
(v)

4
9

Question 2

2.

The sum of the squares of two consecutive odd numbers is 130. Find the numbers

(i)
4

,

6

or

(-4)

,

(-6)
(ii)
8

,

10

or

(-8)

,

(-10)
(iii)
6

,

8

or

(-6)

,

(-8)
(iv)
7

,

9

or

(-7)

,

(-9)
(v)
9

,

12

or

(-9)

,

(-12)

Question 3

3.

The sum of the numerator and denominator of a fraction is
38
.

If
7
is added to both the numerator and denominator,

the fraction is increased by
1
21
. Find the fraction

(i)

21
17
(ii)

17
21
(iii)

19
21
(iv)

5
7
(v)

17
19

Question 4

4.

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

Find the width of the road if its area is equal to the area of the play field

(i)

8.00 m
(ii)

11.00 m
(iii)

12.00 m
(iv)

10.00 m
(v)

9.00 m

Question 5

5.

Find the number which is less than its square by 156

(i)

11
(ii)

14
(iii)

16
(iv)

13
(v)

12

Question 6

6.

The sum of the squares of two consecutive even numbers is 4. Find the numbers

(i)
0

,

2

or

0

,

(-2)
(ii)
(-3)

,

(-1)

or

3

,

1
(iii)
(-2)

,

0

or

2

,

0
(iv)
(-4)

,

(-2)

or

4

,

2
(v)
(-1)

,

1

or

1

,

(-1)

Question 7

7.

The denominator of a fraction exceeds the numerator by
3
.

The square of the fraction is equal to
49
100
. Find the fraction

(i)

7
10
(ii)

1
2
(iii)

9
10
(iv)

7
12
(v)

7
8

Question 8

8.

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

x

+

13

)
days.

Both of them working together can do it in
21

23
87
days. Calculate
x

(i)

38
(ii)

34
(iii)

37
(iv)

36
(v)

39

Question 9

9.

The area of a rectangular room is 216.00 sq.m. If the length and breadth are increased by 3 m, the area would become 315.00 sq.m. Find the original dimensions of the room

(i)

4.00 m , 54.00 m
(ii)

3.00 m , 72.00 m
(iii)

18.00 m , 12.00 m
(iv)

2.00 m , 108.00 m

Question 10

10.

In a two digit number, the unit's digit exceeds it ten's digit by 5 and the product of the given number and the sum of its digits is equal to 112 . Find the number

(i)

38
(ii)

16
(iii)

27
(iv)

49

Question 11

11.

One pipe can fill a cistern in
9
hours less than the other.

The two pipes together can fill it in
10

4
5
hrs.

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

(i)

17 hr , 26 hr
(ii)

16 hr , 25 hr
(iii)

21 hr , 29 hr
(iv)

18 hr , 27 hr
(v)

19 hr , 28 hr

Question 12

12.

Find two natural numbers which differ by 5 and the sum of whose squares is 2393

(i)

(

31

,

36

)
(ii)

(

29

,

35

)
(iii)

(

34

,

39

)
(iv)

(

33

,

38

)
(v)

(

32

,

37

)

Question 13

13.

A stream flows from A to B, a distance of 7.00 km. A man who can row in still water at 8.00 kmph, can row up and down in 2.33 hr . What is the speed of the stream?

(i)

6.00 kmph
(ii)

4.00 kmph
(iii)

2.00 kmph
(iv)

3.00 kmph
(v)

5.00 kmph

Question 14

14.

Twice the square of a number exceeds 5 times the number by 187. Find the number

(i)

8
(ii)

13
(iii)

11
(iv)

12
(v)

10

Question 15

15.

The product of two consecutive odd numbers is 255. Find the numbers

(i)

16 , 18 or -16 , -18
(ii)

17 , 20 or -17 , -20
(iii)

12 , 15 or -12 , -15
(iv)

14 , 16 or -14 , -16
(v)

15 , 17 or -15,-17

Question 16

16.

The perimeter of a rectangular room is 98.00 m and the length of its diagonal is 39.56 m . Find the dimensions of the room

(i)

36.00 m , 13.00 m
(ii)

38.00 m , 11.00 m
(iii)

37.00 m , 12.00 m
(iv)

40.00 m , 9.00 m
(v)

39.00 m , 10.00 m

Question 17

17.

Find the number which exceeds its reciprocal by
18

18
19

(i)

21
(ii)

19
(iii)

16
(iv)

20
(v)

18

Question 18

18.

71 is divided into two parts such that the sum of their reciprocals is
71
1254
.

Find the two parts

(i)

(

33

,

38

)
(ii)

(

31

,

40

)
(iii)

(

35

,

36

)
(iv)

(

34

,

37

)
(v)

(

32

,

39

)

Question 19

19.

A two digit number is such that the product of the digits is 54. When 27 is subtracted from the number, the digits are reversed. Find the number

(i)

96
(ii)

94
(iii)

99
(iv)

97
(v)

95

Question 20

20.

55 is divided into two parts such that the sum of their reciprocals is
55
376
.

Find the two parts

(i)

(

9

,

46

)
(ii)

(

6

,

49

)
(iii)

(

10

,

45

)
(iv)

(

8

,

47

)
(v)

(

7

,

48

)

Question 21

21.

The sum of the ages of a father and his son is 60 years whereas seven years ago, the product of their ages was 273. Find the current ages of the son and the father.

(i)

16 years , 44 years
(ii)

15 years , 45 years
(iii)

13 years , 47 years
(iv)

14 years , 46 years
(v)

12 years , 48 years

Question 22

22.

The area of a rectangular room is 80.00 sq.m. If the length and breadth are increased by 6 m, the area would become 242.00 sq.m. Find the original dimensions of the room

(i)

8.00 m , 10.00 m
(ii)

4.00 m , 20.00 m
(iii)

7.00 m , 11.43 m
(iv)

3.00 m , 26.67 m
(v)

5.00 m , 16.00 m

Question 23

23.

Three consecutive natural numbers are such that the square of the middle number exceeds the difference of the squares of the other two by 60 . Find the three numbers.

(i)

7, 8, 9
(ii)

10, 11, 12
(iii)

9, 10, 11
(iv)

11, 12, 13
(v)

8, 9, 10

Question 24

24.

If the difference of two numbers is 2 and their product is 323, find the numbers

(i)
(-14)

,

(-17)

or

14

,

17
(ii)
(-17)

,

(-19)

or

17

,

19
(iii)
(-19)

,

(-22)

or

19

,

22
(iv)
(-18)

,

(-20)

or

18

,

20
(v)
(-16)

,

(-18)

or

16

,

18

Question 25

25.

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 15 . Find the number

(i)

38
(ii)

41
(iii)

37
(iv)

39
(v)

40

Assignment Key