Unit 7 (Algebra)

24. The distance (in km) travelled in h hours at a constant speed of 40km per hour is __________.

Ans.
The distance (in km) travelled in h hours at a constant speed of 40km per hour is 40h.
From the question,
Time taken to travel a distance = h hours
Travel at a speed of 40 km/h
So, total distance travelled = 40 × h
= 40h

25. p kg of potatoes are bought for Rs 70. Cost of 1kg of potatoes (in Rs) is __________.

Ans.
p kg of potatoes are bought for Rs 70. Cost of 1kg of potatoes (in Rs) is 70/p.
Given, p kg of potatoes are bought for ₹ 70
Then, cost of 1 kg of potato = 70/p

26. An auto rickshaw charges Rs 10 for the first kilometre then Rs 8 for each such subsequent kilometre. The total charge (in Rs) for d kilometres is __________.

Ans.
An auto rickshaw charges Rs 10 for the first kilometre then Rs 8 for each such subsequent kilometre. The total charge (in Rs) for d kilometres is 2 + 8d.
From the question it is given that,
An auto rickshaw charges ₹ 10 for the first kilometre
Then ₹ 8 for each such subsequent kilometre.
So, the total charge (in Rs) for d kilometres is = 10 + (d – 1)8
= 10 + 8d – 8
= 2 + 8d

27. If 7x + 4 = 25, then the value of x is __________.

Ans.
If 7x + 4 = 25, then the value of x is 3.
Consider the equation, 7x + 4 = 25
Transposing 4 from left hand side to right hand side it becomes -4,
7x = 25 – 4
7x = 21
x = 21/7
x = 3

28. The solution of the equation 3x + 7 = –20 is __________.

Ans.
The solution of the equation 3x + 7 = –20 is -9.
Consider the equation, 3x + 7 = –20
Transposing 7 from left hand side to right hand side it becomes -7,
3x = – 20 – 7
3x = – 27
x = -27/3
x = – 9

29. ‘x exceeds y by 7’ can be expressed as __________.

Ans.
‘x exceeds y by 7’ can be expressed as x – y = 7.

30. ‘8 more than three times the number x’ can be written as __________.

Ans.
‘8 more than three times the number x’ can be written as 3x + 8.
As per the condition given in the question, three times the number x = 3x
So, 8 more than three times the number x = 3x + 8

31. Number of pencils bought for Rs x at the rate of Rs 2 per pencil is __________.

Ans.
Number of pencils bought for Rs x at the rate of Rs 2 per pencil is x/2.
From the question it is given that, cost of pencil = ₹ x
No. of pencils bought for ₹ 2 = 1
Therefore, number of pencil bought for ₹ x = ₹ x/2

32. The number of days in w weeks is __________.

Ans.
The number of days in w weeks is 7w.
We know that, there are 7 days in a week.
Therefore, number of days in w weeks is 7w.

33. Annual salary at r rupees per month along with a festival bonus of Rs 2000 is __________.

Ans.
Annual salary at r rupees per month along with a festival bonus of Rs 2000 is ₹12r + 2000.
From the question it is given that,
Salary per month is r rupees
A festival bonus of ₹ 2000
Therefore, the annual salary at r rupees per month along with a festival bonus of Rs 2000 is ₹ 12r + 2000

34. The two digit number whose ten’s digit is ‘t’ and units’s digit is ‘u’ is __________.

Ans.
The two digit number whose ten’s digit is ‘t’ and units’s digit is ‘u’ is 10t + u.
From the question,
Two digit number whose ten’s digit is ‘t’
Two digit number whose unit’s digit is ‘u’
Then, the number = 10 × t + 1 × u
= 10t + u

35. The variable used in the equation 2p + 8 = 18 is __________.

Ans.
The variable used in the equation 2p + 8 = 18 is p.
The word ‘variable’ means something that can vary, i.e., change. The value of a variable is not fixed. We use a variable to represent a number and denote it by any letter such as l, m, n, p, x, y, z etc

36. x metres = __________ centimetres

Ans.
x metres = x × 100 centimetres
We know that, 1 metre = 100 centimetre.
Therefore, x metres × 100 centimetres = 100x centimetres

37. p litres = __________ millilitres

Ans.
p litres = p× 1000 millilitres
we know that, 1 litre = 1000 millilitres
Therefore, p litres × 1000 millilitres = 1000p milliliters.

38. r rupees = __________ paise

Ans.
r rupees = 100r paise
We know that, 1 rupee = 100 paise
Therefore, r rupees = 100r paise

39. If the present age of Ramandeep is n years, then her age after 7 years will be __________.

Ans. If the present age of Ramandeep is n years, then her age after 7 years will be n + 7 years.

40. If I spend f rupees from 100 rupees, the money left with me is __________ rupees.

Ans. If I spend f rupees from 100 rupees, the money left with me is 100 – f rupees.

41. 0 is a solution of the equation x + 1 = 0

Ans.
False. Consider the equation, x + 1 = 0
Then, x = -1

42. The equations x + 1 = 0 and 2x + 2 = 0 have the same solution.

Ans.
True. Consider equations x + 1 = 0
So, x = -1
Consider the equation, 2x + 2 = 0
Divide both the side by 2,
Then we get, x + 1 = 0
Therefore, x = – 1

43. If m is a whole number, then 2m denotes a multiple of 2.

Ans.
True.

44. The additive inverse of an integer x is 2x.

Ans.
False. Additive inverse of x is – x

45. If x is a negative integer, – x is a positive integer.

Ans.
True.

46. 2x – 5 > 11 is an equation.

Ans.
False. An expression with a variable, constants and the sign of equality (=) is called an equation.

47. In an equation, the LHS is equal to the RHS.

Ans.
True

48. In the equation 7k – 7 = 7, the variable is 7.

Ans.
False. In equation 7k – 7 = 7, the variable is k.