Exercise 8.1
Question 1: Write the following using numbers, literals and signs of basic operations. State what each letter represents:
(i) The diameter of a circle is twice its radius.
(ii) The area of a rectangle is the product of its length and breadth.
(iii) The selling price equals the sum of the cost price and the profit.
(iv) The total amount equals the sum of the principal and the interest.
(v) The perimeter of a rectangle is two times the sum of its length and breadth.
(vi) The perimeter of a square is four times its side.
Solution 1:
(i) Let the diameter of a Circle be = d
and radius of a circle be = r
It is given that diameter of a circle is twice its radius.
Thus, d = 2r.
(ii) Let the area of a rectangle be = A
Length of a rectangle be = l
Breadth of a rectangle be = b
It is given that area of a rectangle is the product of its length and breadth.
Thus, A = l × b.
(iii) Let the selling price be = S.P.
Cost price be = C.P.
Profit be = P
It is given that the selling price equals the sum of the cost price and the profit.
Thus, S.P = C.P + P
(iv) Let the amount be = A
Principal be = P
Interest be = I
It is given that the total amount equals the sum of the principal and the interest.
Thus, we get A = P + I
(v) Let perimeter of a rectangle be = P
Length of a rectangle be = l
Breadth of a rectangle be = b
It is given that the perimeter of a rectangle is two times the sum of its length and breadth.
Thus, P = 2 (l + b)
(vi) Let perimeter of a Square be = P
Side of a square be = s
It is given that the perimeter of a square is four times its side.
Thus, P = 4a
Question 2: Write the following using numbers, literals and signs of basic operations:
(i) The sum of 6 and x.
(ii) 3 more than a number y.
(iii) One-third of a number x.
(iv) One-half of the sum of number x and y.
(v) Number y less than a number 7.
(vi) 7 taken away from x.
(vii) 2 less than the quotient of x and y.
(viii) 4 times x taken away from one-third of y.
(ix) Quotient of x by 3 is multiplied by y.
Solution 2:
Question 3: Think of a number. Multiply by 5. Add 6 to the result. Subtract y from this result. What is the result?
Solution 3:
Let the number be x
The number is multiplying by 5 = 5x_______(1)
Add 6 in Equation (1) we get,
= 5x + 6_______(2)
By subtracting y from (2) we get,
= 5x + 6 – y.
Therefore, the result is 5x + 6 – y.
Question 4: The number of rooms on the ground floor of a building is 12 less than the twice of the number of rooms on first floor. If the first floor has x rooms, how many rooms does the ground floor has?
Solution 4:
It is given that the number of the rooms on the first floor = x
Let the number of rooms on the ground floor be = y
Number of rooms on the ground floor of a building is 12 less than the twice of the number of rooms on first floor
Algebraically we can say that,
y = 2x – 12
Thus, the rooms on the ground floor is y = 2x – 12.
Question 5: Binny spend Rs. a daily and saves Rs. b per week. What is her income for two weeks?
Solution 5:
Given,
Amount spent by Binny daily = Rs. a
Total Amount spent by Binny in a week = 7a
Amount saved by Binny weekly= Rs. b
Binny’s income for one week = 7a + b
Binny’s income for 2 weeks = 2(7a + b)
Binny’s income for 2 weeks = Rs. 14a + 2b
Thus, Two weeks income of Binny is Rs. 14a + 2b.
Question 6: Rahul scores 80 marks in English and x marks in Hindi. What is his total score in the two subjects?
Solution 6:
It is given that,
Rahul’s Marks in English = 80
Rahul’s Marks in Hindi = x
Total scores in the two subjects = x + 80
Thus, total score in two subjects getting by Rahul is x + 80.
Question 7: Rohit covers x centimetres in one step. How much distance does he cover in y steps?
Solution 7:
Rohit covered distance in one step = x cm
Distance covered by Rohit in y steps = xy cm
Thus, In y steps Rohit covers xy cm.
Question 8: One apple weighs 75 grams and one orange weighs 40 grams. Determine the weight of x apples and y oranges.
Solution 8:
It is given that,
Weight of one apple is = 75g
Weight of one orange is = 40g
Weight of x apples is = 75g ×x
So the weight of y oranges = 40g ×y
Total weight of x apples and y oranges is = (75x + 40y)g
Question 9: One pencil costs Rs. 2 and one fountain pen costs Rs. 15. What is the cost of x pencils and y fountain pens?
Solution 9:
Cost of a pencil = Rs. 2
Cost of a fountain pen = Rs. 15
Cost of x pencils = 2×x=2x
Cost of y fountain pens = 15×y=15y
The cost of x pencils and y fountain pens = Rs.(2x + 15y)
Exercise 8.2
Question 1: Write each of the following products in exponential form:
(i) a × a × a × a × …….. 15 times
(ii) 8 × b × b × b × a × a × a × a
(iii) 5 × a × a × a × b × b × c × c × c
(iv) 7 × a × a × a …….. 8 times × b × b × b × …… 5 times
(v) 4 × a × a × …… 5 times × b × b × ……. 12 times × c × c …… 15 times
Solution 1:
