Rd Sharma 2019 Solutions for Class 6 Math Chapter 8 Introduction To Algebra are provided here with simple step-by-step explanations. These solutions for Introduction To Algebra are extremely popular among Class 6 students for Math Introduction To Algebra Solutions come handy for quickly completing your homework and preparing for exams. All questions and answers from the Rd Sharma 2019 Book of Class 6 Math Chapter 8 are provided here for you for free. You will also love the ad-free experience on Meritnation’s Rd Sharma 2019 Solutions. All Rd Sharma 2019 Solutions for class Class 6 Math are prepared by experts and are 100% accurate.

Page No 8.11:

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

Answer:

(i) a15(ii) 8b3a4 =8a4b3(iii) 5a3b2c3(iv) 7a8b5(v) 4a5b12c15



Page No 8.12:

Question 2:

Write each of the following in the product form:

(i) a2b5
(ii) 8x3
(iii) 7a3b4
(iv) 15a9b8c6
(v) 30x4y4z5
(vi) 43p10q5r15
(vii) 17p12q20

Answer:

(i) a×a×b×b×b×b×b(ii) 2×2×2×x×x×x(iii) 7×a×a×a×b×b×b×b(iv) 3×5×a×a×a×a×a×a×a×a×a×b×b×b×b×b×b×b×b×c×c×c×c×c×c

(v) 2×3×5×x×x×x×x×y×y×y×y×z×z×z×z×z(vi) 43×p×p×p×p....10 times×q×q....5 times×r×r×r....15 times(vii) 17×p×p×....12 times×q×q×....20 times

Page No 8.12:

Question 3:

Write down each of the following in exponential form:
 
(i) 4a3 × 6ab2 × c2
(ii) 5xy × 3x2y × 7y2
(iii) a3 × 3ab2 × 2a2b2

Answer:

(i) 4×6×a3×a×b2×c2    =24a4b2c2(ii) 5×3×7×x×x2×y×y×y2    =105x3y4(iii) 3×2×a3×a×a2×b2×b2    =6a6b4

Page No 8.12:

Question 4:

The number of bacteria in a culture is x now. If becomes square of itself after one week. What will be its number after two weeks?

Answer:

Present number of bacteria in a culture = x

Number of bacteria in the culture after one week = x2

Number of bacteria in the culture after two weeks = (x2)2 = x4

Page No 8.12:

Question 5:

The area of a rectangle is given by the product of its length and breadth. The length of a rectangle is two-third of its breadth. Find its area if its breadth is x cm.

Answer:

Breadth of the given rectangle = cm

Length of the rectangle = 23x cm
 Area of the rectangle = ​ 23x × x=23x2 cm2

Page No 8.12:

Question 6:

If there are x rows of chairs and each row contains x2 chairs. Determine the total number of chairs.

Answer:

Total number of chairs = Number of rows × Number of chairs in each row
                                 = x×x2=x3



Page No 8.13:

Question 1:

5 more than twice a number x is written as

(a) 5 + x + 2
(b) 2x + 5
(c) 2x − 5
(d) 5x + 2

Answer:

(b) 2x + 5

Page No 8.13:

Question 2:

The quotient of x by 2 is added to 5 is writen as

(a) x2+5
(b) 2x+5
(c) x+25
(d) x2+5

Answer:

(a) x2 + 5

Page No 8.13:

Question 3:

The quotient of x by 3 is multiplied by y is written as

(a) x3y
(b) 3xy
(c) 3yx
(d) xy3

Answer:

(d) xy3
 x3×y = xy3

Page No 8.13:

Question 4:

9 taken away from the sum of x and y is

(a) x + y − 9

(b) 9 − (x+y)

(c) x+y9
(d) 9x+y

Answer:

(a) x + y − 9

Page No 8.13:

Question 5:

The quotient of x by y added ot the product of x and y is written as

(a) xy+xy
(b) yx+xy
(c) xy+xy
(d) xy+yx

Answer:

(a) xy + xy

Page No 8.13:

Question 6:

a2b3 × 2ab2 is equal to

(a) 2a3b4
(b) 2a3b5
(c) 2ab
(d) a3b5

Answer:

(b) 2a3b5

a2b3×2ab2= 2a2×a×b3×b2= 2a3b5

Page No 8.13:

Question 7:

4a2b3 × 3ab2 × 5a3b is equal to

(a) 60a3b5

(b) 60a6b5

(c) 60a6b6

(d) a6b6

Answer:

(c) 60a6b6

 4a2b3×3ab2×5a3b= 4×3×5×a2×a×a3×b3×b2×b= 60a6b6

Page No 8.13:

Question 8:

If 2x2y and 3xy2 denote the length and breadth of a rectangle, the its area is

(a) 6xy
(b) 6x2y2
(c) 6x3y3
(d) x3y3

Answer:

(c) 6x3y3

Area of the rectangle = Length × Breadth
                                =       2x2y×3xy2= 6x3y3

Page No 8.13:

Question 9:

In a room there are x2 rows of chairs and each two contains 2x2 chairs. The total number of chairs in the room is

(a) 2x3
(b) 2x4
(c) x4
(d) x42

Answer:

(b) 2x4
Total number of chairs in the room = Number of rows × Number of chairs in each row
                                                    = x2 × 2x2 = 2x4

Page No 8.13:

Question 10:

a3 × 2a2b × 3ab5 is equal to

(a) a6b6
(b) 23a6b6
(c) 6a6b6
(d) None of these

Answer:

(c) 6a6b6
a3 × 2a2b × 3ab5

= 2×3a3×a2×a×b×b5= 6a(3+2+1)b(1+5)= 6a6b6

Page No 8.13:

Question 1:

Mark the correct alternative in the following question:

9 less than a literal x is written as

(a) 9 - x                           (b) x - 9                           (c) + 9                           (d) None of these

Answer:

Since, 9 less than x is written as x - 9.

Hence, the correct alternative is option (b).

Page No 8.13:

Question 2:

Mark the correct alternative in the following question:

The product of x and y is decreased by 4 is written as

(a) 4 - xy                         (b) x(- 4)                         (c) xy - 4                         (d) xy + 4

Answer:

Since, the product of x and y=xySo, the expression when the product is decreased by 4 is written as xy-4

Hence, the correct alternative is option (c).

Page No 8.13:

Question 3:

Mark the correct alternative in the following question:

The initial count of bacteria is x and it becomes y times every day. The total count of bacteria after one week is

(a) 7xy                                  (b) x + 7y                                  (c) xy7                                  (d) xy6

Answer:

Since, the total count of the bacteria after one week = x×y×y×y×y×y×y=x×y6=xy6

Hence, the correct alternative is option (d).



Page No 8.14:

Question 4:

Mark the correct alternative in the following question:

The product of a and b is added to their sum is written as

(a) ab + a + b                             (b) a + b - ab                             (c) a + ab                            (d) b + ab

Answer:

As, the sum of a and b = a + b
And, the product of a and b = ab

So, the expression when the product is added to the sum = a + b + ab

Hence, the correct alternative is option (a).

Page No 8.14:

Question 5:

Mark the correct alternative in the following question:

x2×2y3×5x3y2 is equal toa 10x2y5                              b 10x5y2                              c 10x5y5                              d x5y5

Answer:

As,

x2×2y3×5x3y2=2×5×x2×x3×y3×y2=10×x2+3×y3+2=10x5y5

Hence, the correct alternative is option (c).

Page No 8.14:

Question 6:

Mark the correct alternative in the following question:

If the lengths of edges of a cuboid are 2x, 3y and 4xy, then its volume is

(a) 24xy                         (b) 9x2y2                         (c) 24x2y2                         (d) 6x2y2

Answer:

As,

Volume of the cuboid=2x×3y×4xy=2×3×4×x×x×y×y=24x2y2

Hence, the correct alternative is option (c).

Page No 8.14:

Question 7:

Mark the correct alternative in the following question:

The sum of a and b is multiplied by taking away 5 from their sum. The expression representing the statement is

(a) (a + b)(a + b - 5)                    (b) (+ b)(5 - - b)                    (c) (+ b)(5 - + b)                    (d) (+ b)(5 + - b)

Answer:

As, the sum of a and b = (a + b)

So, the required expression representing the given statement = (a + b)(a + b - 5)

Hence, the correct alternative is option (a).

Page No 8.14:

Question 8:

Mark the correct alternative in the following question:

The length of a rectangle is y times its breadth x. The area of the rectangle is

(a) xy                         (b) xy2                         (c) x2y                         (d) None of these

Answer:

We have,
Breadth of the rectangle = x and
Length of the rectangle = y × x = xy

Now,
The area of the rectangle = Length × Breadth
= xy × x
= x2y

Hence, the correct alternative is option (c).

Page No 8.14:

Question 9:

Mark the correct alternative in the following question:

2x2×3xy2×4x3y5 is equal toa 24x6y6                        b 24x6y7                        c 24x7y6                        d 24x7y7

Answer:

As,

2x2×3xy2×4x3y5=2×3×4×x2×x×x3×y2×y5=24x6y7

Hence, the correct alternative is option (b).

Page No 8.14:

Question 10:

Mark the correct alternative in the following question:

Thrice x added to y squared is written as

(a) 3xy2                           (b) x2 + y                           (c) x + y2                          (d) 3x + y2

Answer:

As, thrice of x = 3x

And, the square of y = y2

So, the sum of the thrice of x and square of y = 3x + y2

Hence, the correct alternative is option (d).

Page No 8.14:

Question 11:

Write down 7xy2×3x2y×5y4 in the exponential form.

Answer:

7xy2×3x2y×5y4=7×3×5×x×x2×y2×y×y4=105x3y7

Page No 8.14:

Question 12:

The length and breadth of a room are 3x2y3 and 6x3y2, respectively. Find its perimeter and area.

Answer:

We have,Length of the room=3x2y3 andBreadth of the room=6x3y2Now, the perimeter of the room=2×Length+Breadth=2×3x2y3+6x3y2=23x2y3+6x3y2Also, the area of the room=Length×Breadth=3x2y3×6x3y2=3×6×x2×x3×y3×y2=18x5y5

Page No 8.14:

Question 13:

Write down the following in the product form:

i x3y4                          ii 6x7y                          iii 9xy2z2                          iv 10a3b3c3

Answer:

i x3y4=x×x×x×y×y×y×yii 6x7y=6×x×x×x×x×x×x×x×yiii 9xy2z2=9×x×y×y×z×ziv 10a3b3c3=10×a×a×a×b×b×b×c×c×c

Page No 8.14:

Question 14:

The volume of a cuboid is given by the product of its length, breadth and height. The length of a cuboid is 2x2 times its breadth and the height is 32xy times of length. Find the volume of the cuboid if its breadth is 6y2.

Answer:

We have,Breadth of the cuboid=6y2,Length of the cuboid=2x2×Breadth=2x2×6y2=12x2y2 andHeight of the cuboid=32xy×Length=32xy×12x2y2=18x3y3Now, the volume of the cuboid=Length×Breadth×Height=12x2y2×6y2×18x3y3=12×6×18×x2×x3×y2×y2×y3=1296x5y7

Disclaimer: The asnwer given in the textbook is incorrect. The same has been corrected here.

Page No 8.14:

Question 15:

Write 3×a×a×2×b×b×b×c×c×c×c in the exponential form.

Answer:

The exponential form of 3×a×a×2×b×b×b×c×c×c×c is 6a2b3c4.

Page No 8.14:

Question 16:

In a large hall there are 4x2 rows of benches. If each row has 5x2y3 benches and each bench can accomodate xy2 persons, determine the total number of persons if its is full up to its capacity.

Answer:

We have,The number of rows in the hall=4x2,The number of benches in each row=5x2y3 andThe number of persons that can accomodate in a bench=xy2Now, the total number of benches in the hall=4x2×5x2y3=20x4y3So, the number of persons in the hall if it is full up to its capacity=xy2×20x4y3=20x5y5

Page No 8.14:

Question 17:

The cost of painting a rectangular metal sheet is square of its area. If the length and breadth of the rectangle are 2xy and 3x2y, then find the cost. Given that area of a rectangle is the product of its length and breadth.

Answer:

We have,Length of the rectangular metal sheet=2xy andBreadth of the rectangular metal sheet=3x2yNow, the area of the rectangular sheet=Length×Breadth=2xy×3x2y=6x3y2So, the cost of the painting the metal sheet=6x3y22=6x3y2×6x3y2=36x6y4

Page No 8.14:

Question 18:

Ravish covers 3x2y centimetres in one step. What is the distance moved by him in 2xy2 minutes, if he takes xy steps in one minute.

Answer:

We have,The distance covered in one step=3x2y cm,The number of steps taken in one minute=xy andThe time=2xy2 minutesNow, the number of steps taken in 2xy2 minutes=xy×2xy2=2x2y3So, the distance moved in 2xy2 minutes=2x2y3×3x2y=6x4y4 cm

Page No 8.14:

Question 19:

Aarushi spends x daily and saves y per week. How much money she saves in xy2 weeks?

Answer:

We have,Money spent daily=x,Money saved per week=y andNumber of weeks=xy2As, the money spent per week=7×x=7xThe total money saved per week=y-7xSo, the total money saved in xy2 weeks=xy2×y-7x=xy2y-7x

Page No 8.14:

Question 20:

One ball pen costs x and one fountain pen costs y. Find the cost of y2 ball pens and x2 fountain pens.

Answer:

As, the cost of one ball pens=xSo, the cost of y2 ball pens=x×y2=xy2Also, the cost of one fountain pen=ySo, the cost of x2 fountain pens=y×x2=yx2Now, the total cost=xy2+yx2



Page No 8.15:

Question 21:

Fill in the blank:

x + x + x + ... (y times) = _______

Answer:

x + x + x + ... (y times) =  xy 

Page No 8.15:

Question 22:

Fill in the blank:

A chair costs x. The cost of x2y chairs is _______.

Answer:

As, cost of one chair = x

So, the cost of x2y chairs = x×x2y=x3y

Page No 8.15:

Question 23:

Fill in the blank:

a×a×3×b×b×b×2×c×c=_________

Answer:

a×a×3×b×b×b×2×c×c= 6a2b3c2 

Page No 8.15:

Question 24:

Fill in the blank:

A man spends x per week. The total money spent by him in xy2 weeks is _________.

Answer:

As, the money spent in one week = x

So, the total money spent in xy2 weeks =  x×xy2=x2y2 

Page No 8.15:

Question 25:

Fill in the blank:

x3×4xy2×32xy3=_______

Answer:

x3×4xy2×32xy3=4×32×x3×x×x×y2×y3= 6x5y5 



Page No 8.7:

Question 1:

Write the following using numbers, literals and sings 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.

Answer:

(i) Let r and d be the radius and diameter of the circle, respectively. 

 d = 2r


(ii) Let l and b be the length and breadth of the rectangle, respectively.

 Area of rectangle = lb


(iii) Let s, c and p be the selling price, cost price and profit, respectively.

 s = p


(iv) Let T, p and i be the total amount, principal and interest, respectively.

 T = p + i


(v) Let l and b be the length and breadth of the rectangle, respectively.

 Perimeter of rectangle = 2(b)


(vi) Let a be the side of the square.

 Perimeter of  the square = 4a

Page No 8.7:

Question 2:

Write the following using numbers, literals and sings 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 by y.
(viii) 4 time x taken away from one-third of y.
(ix) Quotient of x by 3 is multiplied by y.

Answer:

(i) The sum of 6 and x is 6 + x.
(ii) 3 more than a number y means y + 3.
(iii) One-third of a number x is x3.
(iv) One-half of the sum of numbers x and y is (x+y)2.
(v) Number y less than a number 7 means 7 - y.
(vi) 7 taken away from x means x - 7.
(vii) 2 less than the quotient of x by y is xy-2.
(viii) 4 times x taken away from one-third of y is  y3 - 4x.
(ix) Quotient of x by 3 is multiplied by y means:
 
x3×y= xy3



Page No 8.8:

Question 3:

Think of a number. Multiply it by 5. Add 6 to the result. Subtract y from this result. What is the result?

Answer:

Let the number be x.

On multiplying the number by 5, we get:
5x

​Further, adding 6 to 5x, we get:
5x + 6

Finally, on subtracting y from 5x + 6, we get:
5x + 6 - y

Page No 8.8:

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?

Answer:

Let the number of rooms on the ground floor be y.

It is given that the ​number of rooms on the first floor is x; therefore, we have:

y = 2 × x - ​12 
   = 2x - 12
 
Thus, the number of rooms on the ground floor is 2- 12. 

Page No 8.8:

Question 5:

Binny spends Rs a daily and saves Rs b per week. What is her income for two weeks?

Answer:

It is given that Binny spends Rs. in one day.

 Money spent by him in one week = 7 × a = 7a

It is further given that he saves Rs. in one week; therefor we have:

Total income in one week = Total expenditure in one week + Total saving in one week
                                       = 7a + b

 Binny's total income in 2 weeks = 2 × (7a + b) = Rs. (14a + 2b)

Page No 8.8:

Question 6:

Rahul scores 80 marks in English and x marks in Hindi. What is his total score in the two subject?

Answer:

Marks obtained in English = 80Marks obtained in Hindi = xTotal marks obtained = 80 + x

Page No 8.8:

Question 7:

Rohit covers x centimeters in one step. How much distance does he cover in y steps?

Answer:

It is given that Rohit covers x cm in one step.

 Distance covered by him in ​y steps = x × y = xy cm

Page No 8.8:

Question 8:

One apple weighs 75 grams and one orange weighs 40 grams. Determine the weight of x apples and y oranges.

Answer:

Weight of an apple = 75 gramsWeight of an orange = 40 gramsWeight of x apples = 75×x = 75x gramsWeight of y oranges = 40×y = 40y gramsTotal weight of x apples and y oranges =(75x + 40y) grams

Page No 8.8:

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?

Answer:

Cost of one pencil = Rs. 2
Cost of x pencils = Rs. 2x

Cost of one fountain pen = Rs. 15
Cost of y fountain pens = Rs. 15y

Total cost of x pencils and y fountain pens = Rs. (2x + 15y)



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