2 Marks Questions - Maths STD 8 Questions - Vidyadip

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2 Marks Questions

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17 questions · self-marked practice — reveal the answer and mark yourself.

Question 12 Marks

If a deposit of $Rs 2,000$ earns an interest of $Rs. 500$ in $3$ years, how much interest would a deposit of $Rs 36,000$ earn in $3$ years with the same rate of simple interest?

Answer

In deposit of $Rs. 2000$ earns in $3$ years. with an interest $= Rs.\ 500$
Then, a deposit of $Rs.\ 1000$ earns in $3$ year with an interest = $\frac{500}{2}$ $= Rs. 250$
Similarly, deposit of $Rs. 3600$ i.e., $Rs. 36 \times 1000$ earns in $3$ year with an interest = $250 \times 36 = Rs. 9000$

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Question 22 Marks

There are $20$ grams of protein in $75$ grams of sauted fish. How many grams of protein is in $225\ gm$ of that fish?

Answer

In $20g$ of sauted fish, protein is $75g$ In g of souted fish, protein is $\frac{20}{75}\text{g}$ In $225g$ of sauted fish, protein$=\frac{20}{75}\times255=20\times3=60{\text g}$

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Question 32 Marks

A car travels a distance of $225\ km$ in $25$ litres of petrol. How many litres of petrol will be required to cover a distance of $540$ kilometres by this car?

Answer

A car travels $225\ km$ distance in $25\ L$ of petrol. For $1\ km$,
petrol required $=\frac{25}{225}\text{L}$ For $540\ km$,
the petrol required $=\frac{25}{225}\times540 = 60\text{L}$

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Question 42 Marks

In a hostel of $50$ girls, there are food provisions for $40$ days. If $30$ more girls join the hostel, how long will these provisions last?

Answer

In a hostel of $50$ girls, food are available = $40$ days For $1$ girl, food provisions $= 50 \times 40 = 2000$ days Now, for $(50+30)$ girls i.e., $80$ girls the food provision $=\frac{2000}{80}=\frac{200}{8}=25\text{ days}$

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Question 52 Marks

From the following table, determine if $x$ and $y$ are in direct proportion or not.

$x$	$3$	$6$	$15$	$20$	$30$
$y$	$12$	$24$	$45$	$60$	$120$

Answer

In direct proportion,$\frac{\text{x}}{\text{y}}=\text{k}$(constant) For table $(a)$,

$x$	$3$	$6$	$15$	$20$	$30$
$y$	$12$	$24$	$45$	$60$	$120$

I.e.,$\frac{\text{x}}{\text{y}},\frac{1}{4},\frac{1}{4},\frac{1}{3},\frac{1}{3},\frac{1}{4}$ so, $(a)$ is not in direct proportion.

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Question 62 Marks

A water tank casts a shadow $21\ m$ long. A tree of height $9.5\ m$ casts a shadow $8\ m$ long at the same time. The lengths of the shadows are directly proprotional to their heights. Find the height of the tank.

Answer

The height of the tree $= 9.5m$
The shadow of the tree $= 8m$
The lengths of the shadows are in direct proportion $\frac{8}{9.5}=\frac{21}{\text{x}}$
$\text{x}=\frac{21\times9.5}{8}=\frac{199.5}{8}=24.9375=24.9\text{m}$

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Question 72 Marks

A swimming pool can be filled in $4$ hours by $8$ pumps of the same type. How many such pumps are required if the pool is to be filled in $2\frac{2}{3}$ hours?

Answer

A swimming pool can be filled in $4$ hours by $8$ pumps If we want to fill the swimming pool in $1$ h,
we required $4 \times 8 = 32$ pupmps In $2\frac{2}{3}$ i.e.,$\frac{8}{3}$h the number of pumps required
$=32\div\frac{8}{3}=\frac{32\times3}{8}=4\times3=12\text{ pumps}$

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Question 82 Marks

Sobi types $108$ words in $6$ minutes. How many words would she type in half an hour?

Answer

Sobi can types $108$ words in $6$ min.
In $1$ min, she can type$=\frac{108}{6}=18$ words Thus, in $30$ min, she can type $= 18 \times 30 = 540$ words.

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Question 92 Marks

Ms. Anita has to drive from Jhareda to Ganwari. She measures a distance of $3.5\ cm$ between these villages on the map. What is the actual distance between the villages if the map scale is $1\ cm = 10\ km$?

Answer

The distance between Jhareda to Ganwari in the map $= 3.5\ cm$
Given scale, $1cm = 10\ km$
So, actual distance between the villages $= 35 \times 10 = 35\ km$

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Question 102 Marks

The cost of $27\ kg$ of iron is $Rs\ 1,080$, what will be the cost of $120\ kg$ of iron of the same quality?

Answer

The cost of $27\ kg$ of iron $= Rs.\ 1080$
Cost of $1\ kg$ of iron $=\frac{1080}{27}=$ $RS.\ 40$
The cost of $120\ kg = 40 \times 120 = Rs.\ 4800$
Hence, the cost of $120\ kg$ of iron is $Rs.\ 4800$

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Question 112 Marks

From the following table, determine if x and y are in direct proportion or not.

$X$	$4$	$7$	$10$	$16$
$Y$	$24$	$42$	$60$	$96$

Answer

In direct proportion,$\frac{\text{x}}{\text{y}}=\text{k}$(constant) For table $(b)$,

$X$	$4$	$7$	$10$	$16$
$Y$	$24$	$42$	$60$	$96$

$\frac{1}{6},\frac{1}{6},\frac{1}{6},\frac{1}{6}$ so, $(b)$ is in direct proportion.

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Question 122 Marks

30 persons can reap a field in $17$ days. How many more persons should be engaged to reap the same field in $10$ days?

Answer

$30$ persons can reap a field in $17$ days $1$ person can reap the same field in $30 \times 17 = 510$ days In $10$ days the number of persons required $=\frac{510}{10}=51$ persone

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Question 132 Marks

A recipe for a particular type of muffins requires $1$ cup of milk and $1.5$ cups of chocolates. Riya has $7.5$ cups of chocolates. If she is using the recipe as a guide, how many cups of milk will she need to prepare muffins?

Answer

A particular type of muffins requires $1$ cup of milk & $1.5$ cups of chocolates.
Riya has $7.5$ cups of chocolates.
The number of cups of milk required for $7.5$ cups of chocolate $=\frac{7.5}{1.5}=5\text{ cups}$
Number of cups of milk & chocolates are indirect proportion.

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Question 142 Marks

The variable $x$ is inversely proportional to $y$. If $x$ increases by $p\%$, then by what per cent will $y$ decrease?

Answer

The variable $x$ is inversely proportional to $y$. $xy = k$ (constant) Since, we know that two quantities $x$ and $y$ are said to be in inverse proportion, if an increase in $*$ cause a proportional decrease in $y$ and vice-versa. So, we can say $y$ decrease by $p\%$.

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Question 152 Marks

$44$ cows can graze a field in $9$ days. How many less/more cows will graze the same field in $12$ days?

Answer

$4$ cows can graze a field $= 9$ days The number of cows that can graze the same field in $1$ day $= 44 \times 9$ cows In $12$ days the number of cows required =$=\frac{44\times9}{12}=\frac{44\times3}{4}=11\times3=33\text{ cows}$ Hence, $(44-33)$ i.e., $11$ cows less required for graze the same field in $12$ days.

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Question 162 Marks

A packet of sweets was distributed among $10$ children and each of them received $4$ sweets. If it is distributed among $8$ children, how many sweets will each child get?

Answer

The total number of children $= 10$
If each children received $4$ sweets, then The total number of sweets $= 10 \times 4 = 40$ sweets
If $40$ sweets distributed between $8$ children, then each get $40/8$ i.e. $5$ sweets.

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Question 172 Marks

At a particular time, the length of the shadow of Qutub Minar whose height is $72m$ is $80m$. What will be the height of an electric pole, the length of whose shadow at the same time is $1000\ cm$?

Answer

Length of Qutub Minar $= 72m$ & its shadow at particular time $= 80m$
Length of shadow of electric pole $= 1000\ cm = 10m$
Length of electric pole $=\frac{72}{80}\times10=9\text{m}$

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