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.

#### 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

#### 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

#### Question 3:

Write down each of the following in exponential form:

(i) 4a3 × 6ab2 × c2
(ii) 5xy × 3x2y × 7y2
(iii) a3 × 3ab2 × 2a2b2

#### 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?

Present number of bacteria in a culture = x

Number of bacteria in the culture after one week = ${x}^{2}$

Number of bacteria in the culture after two weeks =

#### 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.

Breadth of the given rectangle = cm

Length of the rectangle = $\frac{2}{3}x$ cm
$\therefore$ Area of the rectangle = ​ cm2

#### Question 6:

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

Total number of chairs = Number of rows $×$ Number of chairs in each row

#### 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

(b) 2x + 5

#### Question 2:

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

(a) $\frac{x}{2}+5$
(b) $\frac{2}{x}+5$
(c) $\frac{x+2}{5}$
(d) $\frac{x}{2+5}$

(a)

#### Question 3:

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

(a) $\frac{x}{3y}$
(b) $\frac{3x}{y}$
(c) $\frac{3y}{x}$
(d) $\frac{xy}{3}$

(d) $\frac{xy}{3}$

#### Question 4:

9 taken away from the sum of x and y is

(a) x + y − 9

(b) 9 − (x+y)

(c) $\frac{x+y}{9}$
(d) $\frac{9}{x+y}$

(a) x + y − 9

#### Question 5:

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

(a) $\frac{x}{y}+xy$
(b) $\frac{y}{x}+xy$
(c) $\frac{xy+x}{y}$
(d) $\frac{xy+y}{x}$

(a)

#### Question 6:

a2b3 × 2ab2 is equal to

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

(b) 2a3b5

#### Question 7:

4a2b3 × 3ab2 × 5a3b is equal to

(a) 60a3b5

(b) 60a6b5

(c) 60a6b6

(d) a6b6

(c) 60a6b6

#### 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

(c) 6x3y3

Area of the rectangle = Length $×$ Breadth
=

#### 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) $\frac{{x}^{4}}{2}$

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

#### Question 10:

a3 × 2a2b × 3ab5 is equal to

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

(c) 6a6b6
a3 × 2a2b × 3ab5

#### 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

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

Hence, the correct alternative is option (b).

#### 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

Hence, the correct alternative is option (c).

#### 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

Since, the total count of the bacteria after one week = $x×y×y×y×y×y×y=x×{y}^{6}=x{y}^{6}$

Hence, the correct alternative is option (d).

#### 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

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).

#### Question 5:

Mark the correct alternative in the following question:

As,

${x}^{2}×2{y}^{3}×5{x}^{3}{y}^{2}\phantom{\rule{0ex}{0ex}}=\left(2×5\right)×\left({x}^{2}×{x}^{3}\right)×\left({y}^{3}×{y}^{2}\right)\phantom{\rule{0ex}{0ex}}=10×{x}^{2+3}×{y}^{3+2}\phantom{\rule{0ex}{0ex}}=10{x}^{5}{y}^{5}$

Hence, the correct alternative is option (c).

#### 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

As,

Hence, the correct alternative is option (c).

#### 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)

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).

#### 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

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).

#### Question 9:

Mark the correct alternative in the following question:

As,

$2{x}^{2}×3x{y}^{2}×4{x}^{3}{y}^{5}\phantom{\rule{0ex}{0ex}}=\left(2×3×4\right)×\left({x}^{2}×x×{x}^{3}\right)×\left({y}^{2}×{y}^{5}\right)\phantom{\rule{0ex}{0ex}}=24{x}^{6}{y}^{7}$

Hence, the correct alternative is option (b).

#### 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

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).

#### Question 11:

$7x{y}^{2}×3{x}^{2}y×5{y}^{4}\phantom{\rule{0ex}{0ex}}=\left(7×3×5\right)×\left(x×{x}^{2}\right)×\left({y}^{2}×y×{y}^{4}\right)\phantom{\rule{0ex}{0ex}}=105{x}^{3}{y}^{7}$

#### Question 12:

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

#### Question 13:

Write down the following in the product form:

#### 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 $\frac{3}{2}$xy times of length. Find the volume of the cuboid if its breadth is 6y2.

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

#### 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.

#### 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.

#### 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.

#### Question 19:

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

#### Question 20:

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

#### Question 21:

Fill in the blank:

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

x + x + x + ... (y times) =  xy

#### Question 22:

Fill in the blank:

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

As, cost of one chair = x

So, the cost of x2y chairs = $\overline{)x×{x}^{2}y=₹{x}^{3}y}$

#### Question 23:

Fill in the blank:

$a×a×3×b×b×b×2×c×c=_________$

#### Question 24:

Fill in the blank:

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

As, the money spent in one week = x

So, the total money spent in xy2 weeks =

#### Question 25:

Fill in the blank:

${x}^{3}×4x{y}^{2}×\frac{3}{2}x{y}^{3}=_______$

#### 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.

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

$\therefore$ d = 2r

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

$\therefore$ Area of rectangle = lb

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

$\therefore$ s = p

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

$\therefore$ T = p + i

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

$\therefore$ Perimeter of rectangle = 2(b)

(vi) Let a be the side of the square.

$\therefore$ Perimeter of  the square = 4a

#### 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.

(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 $\frac{x}{3}$.
(iv) One-half of the sum of numbers x and y is $\frac{\left(x+y\right)}{2}$.
(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 $\frac{x}{y}-2$.
(viii) 4 times x taken away from one-third of y is  .
(ix) Quotient of x by 3 is multiplied by y means:

#### Question 3:

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

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

#### 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?

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.

#### Question 5:

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

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

$\therefore$ 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

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

#### Question 6:

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

#### Question 7:

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

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

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

#### Question 8:

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

#### 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?