EduSahara™ Worksheet

Question 1

1.

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)

39
(iii)

41
(iv)

40
(v)

37

Question 2

2.

Find the number which exceeds its reciprocal by
4

4
5

(i)

6
(ii)

4
(iii)

2
(iv)

5
(v)

8

Question 3

3.

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)

68
(iii)

72
(iv)

71
(v)

70

Question 4

4.

A stream flows from A to B, a distance of 13.00 km. A man who can row in still water at 5.00 kmph, can row up and down in 8.12 hr . What is the speed of the stream?

(i)

2.00 kmph
(ii)

3.00 kmph
(iii)

5.00 kmph
(iv)

4.00 kmph
(v)

1.00 kmph

Question 5

5.

The area of a rectangular room is 120.00 sq.m. If the length and breadth are increased by 3 m, the area would become 207.00 sq.m. Find the original dimensions of the room

(i)

2.00 m , 60.00 m
(ii)

4.00 m , 30.00 m
(iii)

20.00 m , 6.00 m
(iv)

3.00 m , 40.00 m

Question 6

6.

79 is divided into two parts such that the sum of their reciprocals is
79
1560
.

Find the two parts

(i)

(

39

,

40

)
(ii)

(

42

,

37

)
(iii)

(

40

,

39

)
(iv)

(

41

,

38

)
(v)

(

38

,

41

)

Question 7

7.

Twice the square of a number exceeds 5 times the number by 273. Find the number

(i)

13
(ii)

12
(iii)

14
(iv)

11
(v)

16

Question 8

8.

The sum of the squares of two consecutive odd numbers is 74. Find the numbers

(i)
(-7)

,

(-5)

or

7

,

5
(ii)
(-8)

,

(-6)

or

8

,

6
(iii)
(-4)

,

(-3)

or

4

,

3
(iv)
(-6)

,

(-4)

or

6

,

4
(v)
(-10)

,

(-8)

or

10

,

8

Question 9

9.

The sum of the ages of a father and his son is 56 years whereas five years ago, the product of their ages was 205. Find the current ages of the son and the father.

(i)

11 years , 45 years
(ii)

9 years , 47 years
(iii)

8 years , 48 years
(iv)

10 years , 46 years
(v)

12 years , 44 years

Question 10

10.

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

(i)
7

,

9

or

(-7)

,

(-9)
(ii)
6

,

8

or

(-6)

,

(-8)
(iii)
11

,

13

or

(-11)

,

(-13)
(iv)
8

,

10

or

(-8)

,

(-10)
(v)
9

,

11

or

(-9)

,

(-11)

Question 11

11.

If the difference of two numbers is 2 and their product is 143, find the numbers

(i)
11

,

8

or

(-11)

,

(-8)
(ii)
13

,

11

or

(-13)

,

(-11)
(iii)
15

,

14

or

(-15)

,

(-14)
(iv)
14

,

12

or

(-14)

,

(-12)
(v)
12

,

10

or

(-12)

,

(-10)

Question 12

12.

One pipe can fill a cistern in
5
hours less than the other.

The two pipes together can fill it in
7

17
31
hrs.

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

(i)

13 hr , 18 hr
(ii)

16 hr , 20 hr
(iii)

14 hr , 19 hr
(iv)

11 hr , 16 hr
(v)

12 hr , 17 hr

Question 13

13.

The denominator of a fraction exceeds the numerator by
9
.

The square of the fraction is equal to
361
784
. Find the fraction

(i)

19
26
(ii)

3
4
(iii)

17
28
(iv)

19
30
(v)

19
28

Question 14

14.

Find two natural numbers which differ by 16 and the sum of whose squares is 6400

(i)

(

47

,

63

)
(ii)

(

45

,

61

)
(iii)

(

48

,

64

)
(iv)

(

50

,

66

)
(v)

(

49

,

65

)

Question 15

15.

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

x

−

3

)
days.

Both of them working together can do it in
10

30
43
days. Calculate
x

(i)

24
(ii)

23
(iii)

26
(iv)

21
(v)

22

Question 16

16.

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)

26
(ii)

24
(iii)

23
(iv)

22
(v)

25

Question 17

17.

Find the number which is less than its square by 20

(i)

4
(ii)

6
(iii)

5
(iv)

7
(v)

3

Question 18

18.

Three consecutive natural numbers are such that the square of the middle number exceeds the difference of the squares of the other two by 252 . Find the three numbers.

(i)

17, 18, 19
(ii)

18, 19, 20
(iii)

14, 15, 16
(iv)

16, 17, 18
(v)

19, 20, 21

Question 19

19.

The perimeter of a rectangular room is 70.00 m and the length of its diagonal is 28.16 m . Find the dimensions of the room

(i)

28.00 m , 7.00 m
(ii)

25.00 m , 10.00 m
(iii)

26.00 m , 9.00 m
(iv)

29.00 m , 6.00 m
(v)

27.00 m , 8.00 m

Question 20

20.

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

Find the width of the road if its area is
7
6
of the area of the play field

(i)

22.00 m
(ii)

19.00 m
(iii)

20.00 m
(iv)

18.00 m
(v)

21.00 m

Question 21

21.

The sum of the numerator and denominator of a fraction is
22
.

If
4
is added to both the numerator and denominator,

the fraction is increased by
1
24
. Find the fraction

(i)

2
3
(ii)

12
10
(iii)

10
12
(iv)

1

Question 22

22.

The product of two consecutive numbers is 30. Find the numbers

(i)

-7 , -6 or 7 , 6
(ii)

-6 , -5 or 6,5
(iii)

-9 , -7 or 9 , 7
(iv)

-5 , -4 or 5 , 4
(v)

-4 , -3 or 4 , 3

Question 23

23.

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 115 . Find the number

(i)

34
(ii)

23
(iii)

12
(iv)

56
(v)

45

Question 24

24.

A stream flows from A to B, a distance of 12.00 km. A man who can row in still water at 8.00 kmph, can row up and down in 12.80 hr . What is the speed of the stream?

(i)

7.00 kmph
(ii)

5.00 kmph
(iii)

8.00 kmph
(iv)

6.00 kmph
(v)

9.00 kmph

Question 25

25.

The denominator of a fraction exceeds the numerator by
7
.

The square of the fraction is equal to
9
100
. Find the fraction

(i)

1
4
(ii)

3
10
(iii)

1
10
(iv)

3
8
(v)

1
2

Assignment Key