2 Mark Question

Question 12 Marks

In a library 136 copies of a certain book require a shelf-length of 3.4m. How many copies of the same book would occupy a shelf-length of 5.1m?

Answer

Number of copies	136	x
Length the Shelf (in m)	3.4	5.1

Let x be the number of copies that would occupy a shelf-length of 5.1m.
Since the number of copies and the length of the shelf are in direct variation, we have:
$\frac{136}{\text{x}}=\frac{3.4}{\text{5.1}}$
$\Rightarrow 136\times5.1 =\text{x}\times3.4$
$\Rightarrow\text{x}=\frac{136\times5.1}{3.4}$
$= 204$
Thus, 204 copies will occupy a shelf of length 5.1m.

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Question 22 Marks

The second class railway fare for 240 km of Journey is Rs 15.00. What would be the fare for a journey of 139.2km?

Answer

Let Rs x be the fare for a journey of 139.2km.

Distance (in km)	240	139.2
Fare (in Rs.)	15	x

Since the distance travelled and the fare are in direct variation, we have:
$\frac{240}{139.2}=\frac{15}{\text{x}}$
$\Rightarrow 240\times\text{x} =15\times139.2$
$\Rightarrow\text{x}=\frac{15\times139.2}{240}$
$=\frac{2088}{240}$
$= 8.7$
Thus, the fare for a journey of 139.2km will be Rs. 8.70.

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Question 32 Marks

Anupama takes 125 minutes in walking a distance of 100 metre. What distance would she cover in 315 minutes?

Answer

Let the distance travelled in 315 minutes be x km.

Time (in minute):	125	315
Distance (in metre):	100	x

If the distance travelled is more, the time needed to cover it will also be more. Therefore, it is a direct variation.
We get:
125 : 315 = 100 : x
$\Rightarrow\frac{125}{315}=\frac{100}{\text{x}}$
Applying cross multiplication, we get:
$\text{x}=\frac{100\times315}{125}$
=252
Thus, Anupama would cover 252 metre in 315 minutes.

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Question 42 Marks

In which of the following tables x and y vary inversely:

x	9	24	15	3
y	8	3	4	25

Answer

If x and y vary inversely, the product xy should be constant.
Here, product is different for all cases.
Thus, in this case, x and y do not vary inversely.

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Question 52 Marks

If x and y vary inversely as:
x = 30, find y when constant of variation = 900.

Answer

Given:
$\text{x}=30\text{ and k}=900$
$\therefore\text{xy}=\text{k}$
$\Rightarrow30\text{y}=900$
$\Rightarrow\text{y}=\frac{900}{30}$
$=30$
$\therefore\text{y}=30$

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Question 62 Marks

If x and y vary inversely as:
y = 35, find x when constant of variation = 7.

Answer

Given:
y = 35 and k = 7
Now, xy = k
$\Rightarrow35\text{x}=7$
$\Rightarrow\text{x}=\frac{7}{35}$
$=\frac{1}{5}$
$\therefore\text{x}=\frac{1}{5}$

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Question 72 Marks

In which of the following tables x and y vary inversely:

x	4	3	6	1
y	9	12	8	36

Answer

If x and y vary inversely, the product xy should be constant. Here, in one case, product = 6 × 8 = 48 and in the rest, product = 36
Thus, in this case, x and y do not vary inversely.

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Question 82 Marks

Rohit bought 12 registers for Rs 156, find the cost of 7 such registers.

Answer

Let the cost of 7 registers be Rs x.

Register:	12	7
Cost (in Rs.):	156	x

If he buys less number of registers, the cost will also be less. Therefore, it is a direct variation.
We get:
12 : 7 = 156 : x
$\Rightarrow\frac{12}{7}=\frac{156}{\text{x}}$
Applying cross multiplication, we get:
$\text{x}=\frac{156\times7}{12}$
=91
Thus, the cost of such registers will be Rs 91.

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Question 92 Marks

Suneeta types 1080 words in one hour. What is her GWAM (gross words a minute rate)?

Answer

Number of words	1080	x
Time (in minute)	60	1

Let x be her GWAM.
If the time taken is less, GWAM will also be less.
Therefore, it is a direct variation.
1080 : x = 60 : 1
$\Rightarrow\frac{1080}{\text{x}}=\frac{60}{\text{1}}$
Applying cross multiplication, we get:
$\text{x}=\frac{1080\times1}{60}$
$=18$
Thus, her GWAM will be 18.

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Question 102 Marks

A car is travelling at the average speed of 50km/ hr. How much distance would it travel in 12 minutes?

Answer

Distance (in km)	50	x
Time (in minute)	60	12

Let the distance be x km.
If the time taken is less, the distance covered will also be less.
Therefore, it is a direct variation.
50 : x = 60 : 12
$\Rightarrow\frac{50}{\text{x}}=\frac{60}{\text{12}}$
Applying cross multiplication, we get:
$\text{x}=\frac{50\times12}{60}$
$=10$
Thus, the required distance will be 10km.

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Question 112 Marks

In which of the following tables x and y vary inversely:

x	5	20	10	4
y	20	5	10	25

Answer

In all cases, the product xy is constant for any two pairs of values for x and y.
Here, xy = 100 for all cases
Thus, in this case, x and y vary inversely.

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Question 122 Marks

Find the constant of variation from the table given below:

x	3	5	7	9
y	12	20	28	36

Set up a table and solve the following problems. Use unitary method to verify the answer.

Answer

Since it is a direct variation, $\frac{\text{x}}{\text{y}}=\text{k}.$
For x = 3 and y = 12, we have:
$\text{k}=\frac{3}{12}=\frac{1}{4}$
Thus, in all cases, $\text{k}=\frac{1}{4}$

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Question 132 Marks

68 boxes of a certain commodity require a shelf-length of 13.6m. How many boxes of the same commodity would occupy a shelf length of 20.4m?

Answer

Number of Box	68	x
Shelf-length (in m)	13.6	20.4

Let x be the number of boxes that occupy a shelf-length of 20.4m.
If the length of the shelf increases, the number of boxes will also increase.
Therefore, it is a case of direct variation.
$\frac{68}{\text{x}}=\frac{13.6}{\text{20.4}}$
$\Rightarrow 68 \times 20.4 = \text{x}\times13.6$
$\Rightarrow\text{x}=\frac{68\times20.4}{13.6}$
$=\frac{1387.2}{13.6}$
$= 102$
Thus, 102 boxes will occupy a shelf-length of 24.4m.

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Question 142 Marks

In which of the following tables x and y vary inversely:

x	4	3	12	1
y	6	8	2	24

Answer

Since x and y vary inversely, we have:
$\text{y}=\frac{\text{k}}{\text{x}}$
$\Rightarrow\text{xy}=\text{k}$
$\therefore$ The product of x and y is consant
In all cases, the product xy is consant (i.e., 24)
Thus, in this case, x and y vary inversely.

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