2 Marks Questions

Question 12 Marks

A car can cover $270\ km$ in $15$ litres of petrol. How many kilometres will it cover in $8$ litres of petrol$?$

Answer

Distance covered with $15L$ of petrol $= 270\ km$
Distance covered with $1L$ of petrol $=\frac{270}{15}\text{km}$
Distance covered with $8L$ of petrol $=\frac{270}{15}\times8\text{km}=144\text{km}$

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Question 22 Marks

A bus covers a certain distance in $3$ hours $20$ minutes at an average speed of $45\ km$ per hour. How much time will it take to cover the same distance at a speed of $50\ km$ per hour$?$

Answer

Time taken to cover the distance at a speed of $45\ km/ h = 3h\ 20\ min$
Time taken to cover the distance at a speed of $1\ km/ h = 45 × 3.33h $
$[$Less speed, more time taken$]$ $(20$ min $= 0.33$ hour$)$
$\therefore$ Time taken to cover the distance at a speed of $50\ km/ h$
$\frac{45\times3.33}{50}\text{h}\approx3\text{h}$
$[$More speed, less time taken$]$

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Question 32 Marks

If $15$ envelopes cost $Rs.11.25,$ what is the cost of $20$ such envelopes$?$

Answer

Cost of $15$ envelopes $= Rs.11.25$
Cost of $1$ envelope $=\text{Rs.}\frac{11.25}{15}$
$\therefore$ Cost of $20$ envelopes $=\frac{11.25}{15}\times20=\text{Rs. 15}$

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Question 42 Marks

If $\frac{4}{5}$ of a cistern is filled in $1$ minute, how much time will be required to fill the empty cistern$?$

Answer

Time taken to fill $\frac{4}{5}$ of the cistern $= 1\ min$
Time taken to fill $1$ cistern $=\frac{1}{\frac{4}{5}}=\frac{5}{4}=1.25 \ min = 1\ min\ 15 \sec$
Hence, it will take $1\ min\ 15\sec$ to fill the empty cistern.

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Question 52 Marks

If 8kg sugar costs $Rs. 260,$ how much sugar can be bought for $Rs. 877.59?$

Answer

In $Rs. 260,$ the sugar is bought $= 8\ kg$ And in $Rs. 1,$
the sugar is bought $=\frac{8}{260}\text{kg}$
Then in $Rs. 877.50,$
the sugar will be bought $=\frac{8}{260}\times877.50\text{kg}$
$=\frac{8}{260}\times\frac{87750}{100}$
$= 27\text{kg}$

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Question 62 Marks

If $15$ oranges cost $Rs. 110,$ what do $39$ oranges cost$?$

Answer

Cost of $15$ oranges $= Rs. 110$
Cost of $1$ orange $=\text{Rs.}\ \frac{110}{15}$ And
cost of $39$ oranges $=\text{Rs.}\ \frac{110}{15}\times39$
$= Rs. 22 \times 13 = Rs. 286$

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Question 72 Marks

A worker is paid $Rs. 1110$ for $6$ days. If his total wages during a month are $Rs. 4625,$ for how many days did he work$?$

Answer

$Rs. 1110$ is wages for $= 6$ days
$Rs. 1$ will be wages for $=\frac{6}{1110}$ days and
$Rs. 4625$ will be wages for.
$=\frac{6}{1110}\times4625$
$=\frac{1\times6425}{185}=25$ days.

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Question 82 Marks

$24$ cows can graze a field in $20$ days. How many cows can graze it in $15$ days$?$

Answer

Number of cows that graze the field in 20 days $= 24$
Number of cows that graze the field in $1$ day $= 24 \times 20 [$Less days, more cows$]$
$\therefore$ Number of cows that graze the field in $15$ days $\frac{24\times20}{15}=32\text{ cows} [$More days, less cows$]$

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Question 92 Marks

In a fort, $120$ men had provisions for $30$ days. For how many days is the food sufficient for $100$ men$?$

Answer

Number of days with enough food for $120$ men $= 30$
Number of days with enough food for $1$ man $= 30 \times 120 [$Less men, more days$]$
$\therefore$ Number of days with enough food for $100$ men $=\frac{30\times120}{100}=36$
$[$More men, less days$]$

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Question 102 Marks

The cost of $37m$ of silk is $Rs. 6290.$ What length of this silk can be purchased for $Rs. 4420?$

Answer

In $Rs. 6290,$ silk is purchased $= 37m$ And in $Rs. 1,$
silk is purchased $=\frac{37}{6290}\text{m}$ And in $Rs. 4420,$
silk will be purchased $37 =\frac{37}{6290}\times4420\text{m}=26\text{m}$

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Question 112 Marks

If the cost of $8$ toys is $Rs.192,$ what will be the cost of $14$ such toys$?$

Answer

Cost of $8$ toys $= Rs.192$
Cost of $1$ toy $=\text{Rs. }\frac{192}{8}=\text{Rs.}24$
$\therefore$ Cost of $14$ toys $= 24 \times 14 = Rs. 336$

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Question 122 Marks

Travelling $900\ km$ by rail costs $Rs. 2520.$ What would be the fare for a journey of $360\ km$ when a person travels by the same class$?$

Answer

Cost of travelling $900\ km$ is $= Rs. 2520$
And cost of $1\ km$ will be $=\text{Rs. }\frac{2520}{900}$
Andcost of $360\ km$ will be $=\text{Rs. }\frac{2520}{900}\times360$
$=\text{Rs. }1008$

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Question 132 Marks

A car can cover a distance of $357\ km$ on $42$ litres of petrol. How far can it travel on $12$ litres of petrol$?$

Answer

In $42$ litres of petrol, a car covers $= 357\ km$ And in $1$ litre,
car will cover $=\frac{357}{42}\text{km}$ And in $12$ litres,
car will cover $=\frac{357}{42}\times12=102\text{km}$

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