EduSahara™ Worksheet

Question 1

1.

One pipe can fill a cistern in
1
hours less than the other.

The two pipes together can fill it in
2

8
11
hrs.

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

(i)

3 hr , 3 hr
(ii)

6 hr , 7 hr
(iii)

4 hr , 5 hr
(iv)

5 hr , 6 hr
(v)

7 hr , 9 hr

Question 2

2.

Twice the square of a number exceeds 3 times the number by 299. Find the number

(i)

15
(ii)

11
(iii)

13
(iv)

12
(v)

14

Question 3

3.

Find two natural numbers which differ by 16 and the sum of whose squares is 2720

(i)

(

27

,

43

)
(ii)

(

30

,

47

)
(iii)

(

29

,

45

)
(iv)

(

25

,

41

)
(v)

(

28

,

44

)

Question 4

4.

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)

7.50 m
(ii)

5.50 m
(iii)

8.50 m
(iv)

9.50 m
(v)

6.50 m

Question 5

5.

A stream flows from A to B, a distance of 6.00 km. A man who can row in still water at 10.00 kmph, can row up and down in 1.25 hr . What is the speed of the stream?

(i)

2.00 kmph
(ii)

4.00 kmph
(iii)

3.00 kmph
(iv)

0.00 kmph
(v)

1.00 kmph

Question 6

6.

Find the number which is less than its square by 42

(i)

5
(ii)

10
(iii)

8
(iv)

7
(v)

6

Question 7

7.

The perimeter of a rectangular room is 64.00 m and the length of its diagonal is 31.02 m . Find the dimensions of the room

(i)

29.00 m , 3.00 m
(ii)

32.00 m , 0.00 m
(iii)

31.00 m , 1.00 m
(iv)

30.00 m , 2.00 m
(v)

23.00 m , 9.00 m

Question 8

8.

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)

42
(ii)

38
(iii)

39
(iv)

36
(v)

40

Question 9

9.

The product of two consecutive numbers is 306. Find the numbers

(i)

-17 , -16 or 17 , 16
(ii)

-16 , -15 or 16 , 15
(iii)

-20 , -20 or 20 , 20
(iv)

-18 , -17 or 18,17
(v)

-19 , -18 or 19 , 18

Question 10

10.

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

(i)
(-15)

,

(-12)

or

15

,

12
(ii)
(-11)

,

(-9)

or

11

,

9
(iii)
(-12)

,

(-10)

or

12

,

10
(iv)
(-13)

,

(-11)

or

13

,

11
(v)
(-9)

,

(-8)

or

9

,

8

Question 11

11.

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)

25
(ii)

27
(iii)

24
(iv)

23
(v)

22

Question 12

12.

If the difference of two numbers is 5 and their product is 126, find the numbers

(i)
17

,

11

or

(-17)

,

(-11)
(ii)
12

,

7

or

(-12)

,

(-7)
(iii)
15

,

10

or

(-15)

,

(-10)
(iv)
14

,

9

or

(-14)

,

(-9)
(v)
13

,

8

or

(-13)

,

(-8)

Question 13

13.

A two digit number is such that the product of the digits is 21. When 36 is subtracted from the number, the digits are reversed. Find the number

(i)

74
(ii)

75
(iii)

73
(iv)

70
(v)

72

Question 14

14.

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

(i)
(-9)

,

(-7)

or

9

,

7
(ii)
(-8)

,

(-6)

or

8

,

6
(iii)
(-7)

,

(-5)

or

7

,

5
(iv)
(-10)

,

(-8)

or

10

,

8
(v)
(-12)

,

(-9)

or

12

,

9

Question 15

15.

Find the number which exceeds its reciprocal by
15

15
16

(i)

15
(ii)

16
(iii)

14
(iv)

17
(v)

18

Question 16

16.

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 576 . Find the number

(i)

26
(ii)

70
(iii)

48
(iv)

37
(v)

59

Question 17

17.

One pipe can fill a cistern in
8
hours less than the other.

The two pipes together can fill it in
6

29
30
hrs.

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

(i)

11 hr , 19 hr
(ii)

8 hr , 17 hr
(iii)

10 hr , 18 hr
(iv)

12 hr , 20 hr
(v)

14 hr , 21 hr

Question 18

18.

The sum of the ages of a father and his son is 46 years whereas three years ago, the product of their ages was 256. Find the current ages of the son and the father.

(i)

11 years , 35 years
(ii)

12 years , 34 years
(iii)

9 years , 37 years
(iv)

10 years , 36 years
(v)

13 years , 33 years

Question 19

19.

The sum of the numerator and denominator of a fraction is
25
.

If
1
is added to both the numerator and denominator,

the fraction is increased by
1
48
. Find the fraction

(i)

8
15
(ii)

4
5
(iii)

10
15
(iv)

15
10
(v)

10
13

Question 20

20.

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

x

+

20

)
days.

Both of them working together can do it in
6

33
38
days. Calculate
x

(i)

10
(ii)

12
(iii)

9
(iv)

8
(v)

6

Question 21

21.

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
28
(ii)

3
4
(iii)

17
28
(iv)

19
26
(v)

19
30

Question 22

22.

The area of a rectangular room is 448.00 sq.m. If the length and breadth are increased by 2 m, the area would become 544.00 sq.m. Find the original dimensions of the room

(i)

6.00 m , 74.67 m
(ii)

3.00 m , 149.33 m
(iii)

4.00 m , 112.00 m
(iv)

32.00 m , 14.00 m
(v)

7.00 m , 64.00 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 32 . Find the three numbers.

(i)

6, 7, 8
(ii)

10, 11, 12
(iii)

8, 9, 10
(iv)

4, 5, 6
(v)

7, 8, 9

Question 24

24.

A two digit number is such that the product of the digits is 4. When 27 is subtracted from the number, the digits are reversed. Find the number

(i)

40
(ii)

41
(iii)

38
(iv)

42
(v)

43

Question 25

25.

54 is divided into two parts such that the sum of their reciprocals is
54
629
.

Find the two parts

(i)

(

17

,

37

)
(ii)

(

15

,

39

)
(iii)

(

18

,

36

)
(iv)

(

19

,

35

)
(v)

(

16

,

38

)

Assignment Key