1 Marks Question

Question 11 Mark

The weight of $12$ sheets of a paper is $50$ grams. How many sheets will weigh $500$ grams$?$

Answer

Let $x$ be the number of sheets that weigh $500$ gram.

No. of sheets	$12$	$xx$
Weight(in grams)	$50$	$500$

More number of sheets will weigh more. So, it is a case of direct variation. Now, $\frac{12}{50}=\frac{\text{x}}{500}$
$\Rightarrow\text{x}=\frac{12\times500}{50}$
$\Rightarrow\text{x}=120$
$\therefore 120$ sheets will weight $500$ gram.

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Question 21 Mark

If $5$ pipes can fill tank in $144$ minutes, then $6$ pipes can fill it in _______ minutes.

Answer

If $5$ pipes can fill tank in $144$ minutes, then $6$ pipes can fill it in 120 min. Solution: Let $x$ min be the time taken by $6$ pipes to fill the tank.

No. of pipes	$5$	$6$
Time (in min)	$144$	$xx$

Clearly, more number of pipes will take less time to fill the tank. So, it is a case of inverse proportion. Now, $5 \times 144 = 6 \times x$
$\Rightarrow\text{x}=\frac{5\times144}{6}$
$\Rightarrow\text{x} = 120\text{min}$
$\therefore$ 6 pipes can fill the tank in $120\ min.$

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Question 31 Mark

A car covers a certain distance in $1\ hr\ 30$ minutes at $60\ km$ per hour. If it moves at $45\ km$ per hour, it will take _____ hours.

Answer

A car covers a certain distance in $1\ hr\ 30$ minutes at $60\ km$ per hour.
If it moves at $45\ km$ per hour, it will take 2h hours.
Solution:
Let $x$ min be the time taken by the car travelling at $45\ km/ h.$
Now, $1\ h\ 30\ min = (60 + 30)\ min$

Speed(in km/ hr)	$60$	$45$
Time(in min)	$90$	$xx$

Clearly, a car travelling at a less speed will take more time.
So, it is a case of inverse proportion.
Now, $60 \times 90 = 45 \times x$
$\Rightarrow\text{x}=\frac{60\times90}{45}$
$\Rightarrow\text{x}=120\text{min}=2\text{h}$

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Question 41 Mark

If $3$ persons can do a piece of work in $4$ days, then $4$ persons can do it in ______ days.

Answer

If $3$ persons can do a piece of work in $4$ days, then $4$ persons can do it in 3 days.
Solution:
Let $x$ be the number of days taken by $4$ persons to complete the work.

No. of days	$4$	$xx$
No. of persons	$3$	$4$

Clearly, more workers will take less number of days. So, it is a case of inverse proportion. Now, $4 \times 3 = x \times 4$
$\Rightarrow x = 3$ Therefore, $4$ persons can do the piece of work in $3$ days.

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Question 51 Mark

If $8$ oranges cost $Rs. 20.80,$ the cost of $5$ oranges is $Rs.$ ______.

Answer

If $8$ oranges cost $Rs. 20.80,$ the cost of $5$ oranges is $Rs. 13.$
Solution:
Let $Rs. x$ be the cost of $5$ oranges.

No. of oranges	$8$	$5$
Cost of oranges	$20.80$	$xx$

Clearly, less number of oranges will cost less.
So, it is a case of direct variation.
Now, $\frac{8}{20.80}=\frac{5}{\text{x}}$
$\Rightarrow\text{x}=\frac{5\times20.80}{8}$
$\Rightarrow\text{x}=13$
$\therefore$ The cost of $5$ oranges is $Rs.13.$

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