3 Mark Question

Question 13 Marks

The length and breadth of a room are $3 x^2 y^3$ and $6 x^3 y^2$, respectively. Find its perimeter and area.

Answer

We have,
Length of the room $=3 x^2 y^3$ and,
Breadth of the room $=6 x^3 y^2$
Now, the perimeter of the room $=2 \times$ (Length + Breadth)
$=2 \times\left(3 x^2 y^3+6 x^3 y^2\right)$
$=2\left(3 x^2 y^3+6 x^3 y^2\right)$
Also, the area of the room $=$ Length $\times$ Breadth,
$=3 x^2 y^3 \times 6 x^3 y^2$
$=(3 \times 6) \times\left(x^2 \times x^3\right) \times\left(y^3 \times y^2\right)$
$=18 x^5 y^5$

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Question 23 Marks

The volume of a cuboid is given by the product of its length, breadth and height. The length of a cuboid is $2 x^2$ times its breadth and the height is $\frac{3}{2} y x$, times of length. Find the volume of the cuboid if its breadth is $6 y^2$.

Answer

We have,
Breadth of the cuboid $=6 y^2$,
Length of the cuboid $=2 x^2 \times$ Breadth $=2 x^2 \times 6 y^2=12 \times 2 y^2$ and,
Height of the cuboid $=\frac{3}{2} xy \times$ Length $=\frac{3}{2} xy \times 12 x ^2 y ^2=18 x ^3 y ^3$
Now, the volume of the cuboid $=$ Length $\times$ Breadth $\times$ Height,
$=12 x^2 y^2 \times 6 y^2 \times 18 x^3 y^3$
$=(12 \times 6 \times 18) \times\left(x^2 \times x^3\right) \times\left(y^2 \times y^2 \times y^3\right)$
$=1296 x^5 y^7$

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Question 33 Marks

One ball pen costs Rs. $x$ and one fountain pen costs Rs. $y$. Find the cost of $y^2$ ball pens and $x^2$ fountain pens.

Answer

As, the cost of one ball pens = Rs. $x$
So, the cost of $y^2$ ball pens $=x \times y^2=$ Rs. $x^2$
Also, the cost of one fountain pen $=$ Rs. $y$
So, the cost of $x^2$ fountain pens $=y \times x^2=$ Rs. $y x^2$
Now, the total cost $=$ Rs. $\left(x y^2+y^2\right)$

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Question 43 Marks

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. a in one day.
$\therefore$ Money spent by him in one week = 7 × a = 7a
It is further given that he saves Rs. b in one week; therefore 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)

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Question 53 Marks

The cost of painting a rectangular metal sheet is square of its area. If the length and breadth of the rectangle are $2xy$ and $3x^2y,$ 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 $= 2xy$ and,
Breadth of the rectangular metal sheet $= 3x^2y$
Now, the area of the rectangular sheet = Length $\times$ Breadth,
$= 2xy \times 3x^2y$
$= 6x^3y^2$
So, the cost of the painting the metal sheet = $(6x^3y^2)^2= 6x^3y^2\times 6x^3y^2= 36x^6y^4.$

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Question 63 Marks

Aarushi spends Rs. x daily and saves Rs. y per week. How much money she saves in $xy^2$ weeks?

Answer

We have,
Money spent daily = Rs. $x$,
Money saved per week = Rs. $y$ and,
Number of weeks $=x y^2$
As, the money spent per week $=7 \times x=$ Rs. $7 x$
$\Rightarrow$ The total money saved per week $=$ Rs. $(y-7 x)$
So, the total money saved in $x y^2$ weeks $=x y^2 \times(y-7 x)=$ Rs. $x y^2(y-7 x)$

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Question 73 Marks

Ravish covers $3 x^2 y$ centimetres in one step. What is the distance moved by him in $2 x y^2$ minutes, if he takes $x y$ steps in one minute.

Answer

We have,
The distance covered in one step $=3 x^2 y cm$,
The number of steps taken in one minute $=x y$ and
The time $=2 x y^2$ minutes,
Now, the number of steps taken in $2 x y^2$ minutes $=x y \times 2 x y^2=2 x^2 y^3$
So, the distance moved in $2 x y^2$ minutes $=2 x^2 y^3 \times 3 x^2 y=6 x^4 y^4 cm$.

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Question 83 Marks

In a large hall there are $4 x^2$ rows of benches. If each row has $5 x^2 y^3$ benches and each bench can accomodate $x y^2$ 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 $=4 x^2$,
The number of benches in each row $=5 x^2 y^3$ and,
The number of persons that can accomodate in a bench $=x y^2$
Now, the total number of benches in the hall $=4 x^2 \times 5 x^2 y^3=20 x^4 y^3$
So, the number of persons in the hall if it is full up to its capacity $=x y^2 \times 20 x^4 y^3=20 x^5 y^5$.

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