EduSahara™ Worksheet

Question 1

1.

Twice the square of a number exceeds 5 times the number by 322. Find the number

(i)

15
(ii)

13
(iii)

11
(iv)

16
(v)

14

Question 2

2.

Find the number which exceeds its reciprocal by
9

9
10

(i)

9
(ii)

10
(iii)

8
(iv)

11
(v)

13

Question 3

3.

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

(i)
(-8)

,

(-6)

or

8

,

6
(ii)
(-6)

,

(-5)

or

6

,

5
(iii)
(-9)

,

(-7)

or

9

,

7
(iv)
(-10)

,

(-8)

or

10

,

8
(v)
(-12)

,

(-9)

or

12

,

9

Question 4

4.

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)

37
(iv)

39
(v)

42

Question 5

5.

The sum of the squares of two consecutive even numbers is 340. Find the numbers

(i)
(-14)

,

(-12)

or

14

,

12
(ii)
(-16)

,

(-15)

or

16

,

15
(iii)
(-11)

,

(-9)

or

11

,

9
(iv)
(-15)

,

(-13)

or

15

,

13
(v)
(-13)

,

(-11)

or

13

,

11

Question 6

6.

A stream flows from A to B, a distance of 5.00 km. A man who can row in still water at 8.00 kmph, can row up and down in 1.67 hr . What is the speed of the stream?

(i)

3.00 kmph
(ii)

5.00 kmph
(iii)

2.00 kmph
(iv)

6.00 kmph
(v)

4.00 kmph

Question 7

7.

The denominator of a fraction exceeds the numerator by
2
.

The square of the fraction is equal to
361
441
. Find the fraction

(i)

1
(ii)

19
21
(iii)

19
23
(iv)

17
21

Question 8

8.

In a two digit number, the unit's digit exceeds it ten's digit by 3 and the product of the given number and the sum of its digits is equal to 754 . Find the number

(i)

58
(ii)

69
(iii)

47
(iv)

80
(v)

36

Question 9

9.

The sum of the ages of a father and his son is 66 years whereas eleven years ago, the product of their ages was 123. Find the current ages of the son and the father.

(i)

15 years , 51 years
(ii)

13 years , 53 years
(iii)

12 years , 54 years
(iv)

14 years , 52 years
(v)

16 years , 50 years

Question 10

10.

The area of a rectangular room is 288.00 sq.m. If the length and breadth are increased by 8 m, the area would become 624.00 sq.m. Find the original dimensions of the room

(i)

18.00 m , 16.00 m
(ii)

2.00 m , 144.00 m
(iii)

4.00 m , 72.00 m
(iv)

3.00 m , 96.00 m

Question 11

11.

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

The two pipes together can fill it in
4

2
7
hrs.

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

(i)

5 hr , 14 hr
(ii)

9 hr , 17 hr
(iii)

6 hr , 15 hr
(iv)

3 hr , 13 hr
(v)

7 hr , 16 hr

Question 12

12.

The denominator of a fraction exceeds the numerator by
5
.

The square of the fraction is equal to
1
36
. Find the fraction

(i)

1
2
(ii)

1
6
(iii)

1
4
(iv)

1
8
(v)

(
-1
6
)

Question 13

13.

Find two natural numbers which differ by 10 and the sum of whose squares is 2938

(i)

(

34

,

44

)
(ii)

(

36

,

45

)
(iii)

(

32

,

42

)
(iv)

(

33

,

43

)
(v)

(

30

,

41

)

Question 14

14.

The perimeter of a rectangular room is 46.00 m and the length of its diagonal is 17.00 m . Find the dimensions of the room

(i)

15.00 m , 8.00 m
(ii)

14.00 m , 9.00 m
(iii)

16.00 m , 7.00 m
(iv)

13.00 m , 10.00 m
(v)

17.00 m , 6.00 m

Question 15

15.

Three consecutive natural numbers are such that the square of the middle number exceeds the difference of the squares of the other two by 45 . Find the three numbers.

(i)

7, 8, 9
(ii)

9, 10, 11
(iii)

10, 11, 12
(iv)

8, 9, 10
(v)

6, 7, 8

Question 16

16.

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

x

+

14

)
days.

Both of them working together can do it in
3

23
24
days. Calculate
x

(i)

4
(ii)

6
(iii)

7
(iv)

5
(v)

2

Question 17

17.

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

(i)
10

,

12

or

(-10)

,

(-12)
(ii)
12

,

14

or

(-12)

,

(-14)
(iii)
9

,

11

or

(-9)

,

(-11)
(iv)
13

,

15

or

(-13)

,

(-15)
(v)
11

,

13

or

(-11)

,

(-13)

Question 18

18.

If the difference of two numbers is 2 and their product is 168, find the numbers

(i)
(-12)

,

(-14)

or

12

,

14
(ii)
(-10)

,

(-11)

or

10

,

11
(iii)
(-13)

,

(-15)

or

13

,

15
(iv)
(-11)

,

(-13)

or

11

,

13
(v)
(-15)

,

(-17)

or

15

,

17

Question 19

19.

The sum of the numerator and denominator of a fraction is
37
.

If
2
is added to both the numerator and denominator,

the fraction is increased by
7
264
. Find the fraction

(i)

17
22
(ii)

3
4
(iii)

15
22
(iv)

22
15
(v)

13
22

Question 20

20.

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

Find the width of the road if its area is
3
4
of the area of the play field

(i)

0.50 m
(ii)

3.50 m
(iii)

1.50 m
(iv)

2.50 m
(v)

4.50 m

Question 21

21.

Twice the square of a number exceeds 4 times the number by 16. Find the number

(i)

4
(ii)

2
(iii)

6
(iv)

5
(v)

3

Question 22

22.

The product of two consecutive even numbers is 80. Find the numbers

(i)

7 , 9 or -7 , -9
(ii)

6 , 8 or -6 , -8
(iii)

11 , 12 or -11 , -12
(iv)

8 , 10 or -8,-10
(v)

9 , 11 or -9 , -11

Question 23

23.

Find the number which is less than its square by 380

(i)

21
(ii)

22
(iii)

20
(iv)

19
(v)

18

Question 24

24.

A two digit number is such that the product of the digits is 9. When 72 is added to the number, the digits are reversed. Find the number

(i)

18
(ii)

21
(iii)

20
(iv)

16
(v)

19

Question 25

25.

45 is divided into two parts such that the sum of their reciprocals is
45
86
.

Find the two parts

(i)

(

43

,

2

)
(ii)

(

45

,

0

)
(iii)

(

42

,

3

)
(iv)

(

41

,

4

)
(v)

(

44

,

1

)

Assignment Key