EduSahara™ Worksheet

Question 1

1.

The denominator of a fraction exceeds the numerator by
7
.

The square of the fraction is equal to
1
4
. Find the fraction

(i)

5
14
(ii)

7
12
(iii)

1
2
(iv)

9
14
(v)

7
16

Question 2

2.

The sum of the numerator and denominator of a fraction is
26
.

If
6
is added to both the numerator and denominator,

the fraction is increased by
72
475
. Find the fraction

(i)

5
19
(ii)

9
19
(iii)

7
17
(iv)

7
19
(v)

19
7

Question 3

3.

The sum of the squares of two consecutive even numbers is 20. Find the numbers

(i)
2

,

4

or

(-2)

,

(-4)
(ii)
1

,

3

or

(-1)

,

(-3)
(iii)
4

,

7

or

(-4)

,

(-7)
(iv)
(-1)

,

2

or

1

,

(-2)
(v)
3

,

5

or

(-3)

,

(-5)

Question 4

4.

Find two natural numbers which differ by 3 and the sum of whose squares is 689

(i)

(

14

,

17

)
(ii)

(

17

,

20

)
(iii)

(

18

,

21

)
(iv)

(

19

,

23

)
(v)

(

16

,

19

)

Question 5

5.

The sum of the squares of two consecutive even numbers is 724. Find the numbers

(i)
17

,

19

or

(-17)

,

(-19)
(ii)
18

,

20

or

(-18)

,

(-20)
(iii)
20

,

23

or

(-20)

,

(-23)
(iv)
15

,

17

or

(-15)

,

(-17)
(v)
19

,

21

or

(-19)

,

(-21)

Question 6

6.

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)

40
(iii)

41
(iv)

36
(v)

39

Question 7

7.

Find the number which exceeds its reciprocal by
14

14
15

(i)

13
(ii)

14
(iii)

15
(iv)

16
(v)

18

Question 8

8.

The sum of the ages of a father and his son is 49 years whereas three years ago, the product of their ages was 190. Find the current ages of the son and the father.

(i)

9 years , 40 years
(ii)

7 years , 42 years
(iii)

8 years , 41 years
(iv)

10 years , 39 years
(v)

6 years , 43 years

Question 9

9.

Three consecutive natural numbers are such that the square of the middle number exceeds the difference of the squares of the other two by 320 . Find the three numbers.

(i)

22, 23, 24
(ii)

19, 20, 21
(iii)

18, 19, 20
(iv)

20, 21, 22
(v)

17, 18, 19

Question 10

10.

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

x

+

15

)
days.

Both of them working together can do it in
18

40
77
days. Calculate
x

(i)

32
(ii)

34
(iii)

30
(iv)

31
(v)

28

Question 11

11.

The sum of the squares of two consecutive odd numbers is 290. Find the numbers

(i)
(-14)

,

(-12)

or

14

,

12
(ii)
(-11)

,

(-8)

or

11

,

8
(iii)
(-12)

,

(-10)

or

12

,

10
(iv)
(-13)

,

(-11)

or

13

,

11
(v)
(-16)

,

(-13)

or

16

,

13

Question 12

12.

A play field is
50.00 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
11
10
of the area of the play field

(i)

10.00 m
(ii)

8.00 m
(iii)

9.00 m
(iv)

11.00 m
(v)

12.00 m

Question 13

13.

The area of a rectangular room is 56.00 sq.m. If the length and breadth are increased by 5 m, the area would become 171.00 sq.m. Find the original dimensions of the room

(i)

7.00 m , 8.00 m
(ii)

8.00 m , 7.00 m
(iii)

6.00 m , 9.33 m
(iv)

14.00 m , 4.00 m

Question 14

14.

Find two natural numbers which differ by 20 and the sum of whose squares is 6928

(i)

(

46

,

65

)
(ii)

(

51

,

71

)
(iii)

(

47

,

67

)
(iv)

(

48

,

68

)
(v)

(

49

,

69

)

Question 15

15.

A stream flows from A to B, a distance of 7.00 km. A man who can row in still water at 6.00 kmph, can row up and down in 2.62 hr . What is the speed of the stream?

(i)

1.00 kmph
(ii)

2.00 kmph
(iii)

4.00 kmph
(iv)

3.00 kmph
(v)

0.00 kmph

Question 16

16.

The product of two consecutive numbers is 240. Find the numbers

(i)

-13 , -13 or 13 , 13
(ii)

-17 , -16 or 17 , 16
(iii)

-18 , -17 or 18 , 17
(iv)

-16 , -15 or 16,15
(v)

-15 , -14 or 15 , 14

Question 17

17.

One pipe can fill a cistern in
6
hours less than the other.

The two pipes together can fill it in
8

4
17
hrs.

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

(i)

15 hr , 21 hr
(ii)

16 hr , 22 hr
(iii)

13 hr , 19 hr
(iv)

11 hr , 18 hr
(v)

14 hr , 20 hr

Question 18

18.

Twice the square of a number exceeds 2 times the number by 420. Find the number

(i)

(-13)
(ii)

(-14)
(iii)

(-12)
(iv)

(-15)
(v)

(-16)

Question 19

19.

52 is divided into two parts such that the sum of their reciprocals is
13
88
.

Find the two parts

(i)

(

46

,

6

)
(ii)

(

44

,

8

)
(iii)

(

43

,

9

)
(iv)

(

42

,

10

)
(v)

(

45

,

7

)

Question 20

20.

A two digit number is such that the product of the digits is 7. When 54 is subtracted from the number, the digits are reversed. Find the number

(i)

74
(ii)

70
(iii)

72
(iv)

68
(v)

71

Question 21

21.

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 405 . Find the number

(i)

23
(ii)

45
(iii)

67
(iv)

56
(v)

34

Question 22

22.

If the difference of two numbers is 2 and their product is 399, find the numbers

(i)
(-16)

,

(-19)

or

16

,

19
(ii)
(-19)

,

(-21)

or

19

,

21
(iii)
(-22)

,

(-24)

or

22

,

24
(iv)
(-20)

,

(-22)

or

20

,

22
(v)
(-18)

,

(-20)

or

18

,

20

Question 23

23.

Find the number which is less than its square by 210

(i)

16
(ii)

15
(iii)

17
(iv)

12
(v)

14

Question 24

24.

The perimeter of a rectangular room is 78.00 m and the length of its diagonal is 30.08 m . Find the dimensions of the room

(i)

27.00 m , 12.00 m
(ii)

28.00 m , 11.00 m
(iii)

30.00 m , 9.00 m
(iv)

29.00 m , 10.00 m
(v)

26.00 m , 13.00 m

Question 25

25.

Find the number which exceeds its reciprocal by
15

15
16

(i)

17
(ii)

19
(iii)

14
(iv)

16
(v)

15

Assignment Key