Question 13 Marks
A train covers a distance of $51\ km$ in $45$ minutes. How long will it take to cover $221\ km?$
AnswerTo cover a distance of $51\ km,$
time is taken $= 45$ minutes
$=\frac{3}{4}$ hours
To cover a distance of $1\ km,$ time will be
Taken $=\frac{3}{4\times51}$ hours
And to cover a distance of $221\ km$ time
Will be $=\frac{3\times221}{4\times51}=\frac{1\times221}{4\times17}$
$=\frac{1\times13}{4}=\frac{13}{4}$ hours $=3\frac{1}{4}$ hours
$= 3$ hours $15$ minutes.
View full question & answer→Question 23 Marks
If $22.5$ metres of a uniform iron rod weighs $85.5\ kg,$ what will be the length of $22.8\ kg$ of the same rod$?$
AnswerIf weight is $85.5\ kg,$ then length of iron rod $= 22.5m$
If weight is $1\ kg,$ then length of rod will be $=\frac{22.5}{85.5}\text{m}$ And if weight is $22,8\ kg,$
then length of rod will be $=\frac{22.5\times22.8}{85.5}\text{m}$
$=\frac{225\times228\times10}{10\times855\times10}\text{m}$
$=\frac{45\times228}{2\times855}\text{m}$
$=\frac{1\times114}{1\times19}=6\text{m}$
View full question & answer→Question 33 Marks
Reeta type $40$ words per minute and takes $24$ minutes to type a certain document. Her friend Geeta has a typing speed of $48$ words per minute. In how much time, will she be able to type the same document?
AnswerTime taken to type $40$ words per minute $= 24$ min
Time taken to type a word per minute $= 24 \times 40$ min
Now, time taken to type $48$ words per minute $=\frac{24\times40}{48}=20\text{ min}$
Hence, Geeta will take $20$ minutes to type the same document if her typing speed is $48$ words/ min.
View full question & answer→Question 43 Marks
A girl can finish a book in $25$ days if she reads $18$ pages of it every day. How many days will she take to finish it, if she reads $15$ pages every day$?$
AnswerDays taken to finish the book if $18$ pages are read everyday $= 25$ Days taken to finish the book if $1$ page is read everyday $= 18 × 25$ [less pages, more days] Now, days taken to finish the book if $15$ pages are read everyday $=\frac{18\times25}{15}=30$ [more pages, less days] Hence, the girl will take $30$ days to finish the book if she reads $15$ pages everyday.
View full question & answer→Question 53 Marks
If $48$ men can dig a trench in $14$ days. how long will $28$ men take to dig a similar trench$?$
Answer$48$ men can dig a trench in $14$ days. $1$ man can dig the trench in $14 × 48$ days. [less men, more days] Therefore, $28$ men can dig the trench in $\frac{14\times48}{28}\text{days}=24$ days $[$more men, less days$]$
Hence, $28$ men will take $24$ days to dig a similar trench.
View full question & answer→Question 63 Marks
At a particular time of a day, $7m-$high flagstaff casts a shadow which is $8.2m$ long. What is the height of the building which casts a shadow $20.5$ metres in length at the same moment?
AnswerIf length of shadow is $8.2m,$ then
Height of flag staff is $= 7m$
If length of shadow is $1m,$ then height will be
$=\frac{7}{8.2}\text{m}$
And if length of shadow is $20.5m,$ then height will be
$=\frac{7}{8.2}\times20.5=\frac{7\times5}{2}$
$=\frac{35}{2}\text{m}=17.5\text{m}$
View full question & answer→Question 73 Marks
$1152$ bars of soap can be packed in $8$ cartons of the same size. How many such cartons will be required to pack $3888$ bars$?$
Answer$1152$ bars of soap can be packed in $8$ cartons $1$ bar of soap coil be packed in.
$=\frac{8}{1152}$ cartons And $3888$ bars of soap will be packed in
$=-\frac{8\times3888}{1152}$ cartons
$=\frac{1\times3888}{144}=27$ cartons.
View full question & answer→Question 83 Marks
A bus covers a certain distance in $3$ hours $20$ minutes at an average speed $45\ km/ h.$ How long will it take to cover the same distance at a speed of $36\ km/ h?$
AnswerTime taken to cover the distance at a speed of $45\ km/ h = 3\ h$
$20 \min = 200 \min$ Time taken to cover the distance at a speed of $1\ km/ h = 45 × 3.33 \min$
[less speed, more time Time taken to cover the distance at a speed of $36\ km/ h$
$=\frac{45\times3.33}{36}= 4.1625 \text{h} \approx 4 \text{h } 10$
Hence, the bus will take $4\ h\ 10 \min$ to cover the distance if its speed is $36\ km/h.$
View full question & answer→Question 93 Marks
$16$ men can reap a field in $30$ days. How many men must be engaged to reap the same field in $24$ days?
AnswerNo. of men required to reap the field in $30$ days $= 16$
No. of men required to reap the field in $1$ day $= 16 \times 30 ($less days, more men$) $
Now, no. of men required to reap the field in $24$ days $=\frac{16\times30}{24}=20$ (more days, less men)
$\therefore 20$ men are required to reap the field in $24$ days.
View full question & answer→Question 103 Marks
$15$ men can build a $16.25m$ long wall up to a certain height in one day. How many men should be employed to build a wall of same height but of length $26$ metres in one day$?$
Answer$16.25m$ long wall is build by $= 15$ men $I\ m$ long wall will be built by $=\frac{15}{16.25}\text{m}$ And $26m$ long wall be build by $=\frac{15\times26}{16.25}$
$=\frac{15\times26\times100}{1625}=3\times2\times4=24\text{ men}$
View full question & answer→Question 113 Marks
A group of $120$ men had provisions for $200$ days. After $5$ days, $30$ men died due to an epidemic. How long will the remaining food last$?$
AnswerNumber of days for which the food is sufficient for $120$ men $= 195$
Number of days for which food is sufficient for $1$ man $= 120 \times 195$
Number of days for which food is sufficient for $90$ men $=\frac{120\times195}{90}=260$
Hence, the food will last for $260$ days.
View full question & answer→Question 123 Marks
In a hospital, the monthly consumption of milk of $60$ patients is $1350$ litres. How many patients can be accommodated in the hospital if the monthly ration of milk is raised to $1710$ litres assuming that the quota per head remains the same$?$
Answer$1350$ litres of milk cm be consumed by $= 60$
patients $1$ litres of milk can be consumed by $=\frac{60}{1350}$
patients and $1710$ litres of milk can be consumed $\text{by}=\frac{60\times1710}{1350}$
$=\frac{2\times1710}{45}=2\times38$
$=76$ patients.
View full question & answer→Question 133 Marks
If the weight of 6 sheets of a paper is $162$ grams, how many sheets of the same quality of paper would weigh $13.5\ kg?$
AnswerIn $162$ grams, sheets are $= 6$ In $1\ gm$
sheets will be $=\frac{6}{162}$ And in $13.5\ kg$ or $13500\ gms,$
sheets will be $=\frac{6\times13500}{162}$
$=\frac{1\times13500}{27}=500$ sheets.
View full question & answer→Question 143 Marks
$45$ cows can graze a field in $13$ days. How many cows will graze the same field in $9$ days$?$
AnswerNumber of cows that can graze the field in $13$ days $= 45$
Number of cows that can graze the field in $1$ day $= 45 × 13 [$Less days, more cows$]$
Therefore, number of cows that can graze the field in $9$ days $=\frac{45\times13}{9}=65$ [More days, less cows]
Hence, $65$ cows can graze the field in $9$ days.
View full question & answer→Question 153 Marks
A contractor employed $210$ men to build a house in $60$ days. After $12 $days, he was joined by $70$ more men. In how many days will the remaining work be finished$?$
AnswerInitially, the contractor had $210$ men for $60$ days.
After $12$ days, $70$ more men joined.
$210$ men can finish the work in $48$ days $1$ man can finish the work in $210 × 48$ days
Now, $280$ men can finish the work in $=\frac{210\times48}{280}\text{days}=36\text{ days}$
Hence, it will take $36$ days to finish the remaining work.
View full question & answer→Question 163 Marks
If the thickness of a pile of $16$ cardboards is $44\ mm$ how many cardboards will be there in a pile which is $71.5\ cm$ thick$?$
AnswerIn $44\ mm$ of thickness, cardboards are $= 16$
In $1\ mm$ of thickness, cardboards will be $=\frac{16}{44}$ And in $71.5\ cm$ or $7.15\ mm$ cardboards will be $=\frac{16\times715}{44}=\frac{4\times715}{11}=4\times65$ 260 cardboards.
View full question & answer→Question 173 Marks
$16$ horses can consume a certain quantity of corn in $25$ days. In how many days would the same quantity be consumed by $40$ horses$?$
AnswerTime taken by $16$ horses to consume the corn $= 25$ days
Time taken by $1$ horse to consume the corn $= 25 \times 16 [$less horses, more time taken$]$
Time taken by $40$ horses to consume the corn $=\frac{25\times16}{40}=10\text{ days}$ [more horses, less time taken]
Hence, $40$ horses would consume the same quantity of corn in $10$ days.
View full question & answer→Question 183 Marks
The extension of an elastic string varies directly as the weight hung on it. If a weight of $150\ g$ produces an extension of $2.8\ cm,$ what weight would produce an extension of. $19.6\ cm?$
Answer$2.8\ cm$ extension is produced by $= 150\ g.$
$1\ cm$ extension will be produced by $=\frac{150}{2.8}\text{g}$ and $19.6\ cm$ extension will be produced by $=\frac{150\times19.6}{2.8}\text{g}=\frac{150\times196\times10}{10\times28}\text{g}$
$=\frac{150\times196}{28}=150\times7\text{g}$
$=1\text{kg }50\text{g.}$
View full question & answer→Question 193 Marks
A military camp has provisions for $360$ men to last for $25$ days. How many men must be transferred to another camp so that the food lasts for $30$ days?
AnswerNo. of men for which the provision will last for $25$ days $= 360$
No. of men for which the provision will last for $1$ day $= 360 × 25$
Now, no. of men for which the provision will last for $30$ days $=\frac{360\times25}{30}=300$
$\therefore 60$ men, i.e., $(360 − 300),$ must be transferred to another camp so that the provision lasts for $30$ days.
View full question & answer→Question 203 Marks
At the beginning of a month, a factory has enough materials to make $240$ tonnes of steel in a month. If $60$ more tonnes of steel is to be made that month, how long will the materials last$?$
AnswerTime taken to make $240$ tonnes of steel $= 30$ days
Time taken to make $1$ tonne of steel $= 30 \times 240$ days
Now, time taken to make $300$ or $(240 + 60)$ tonnes of steel $=\frac{30\times240}{300}=24\text{ days}$
$\therefore$ The materials will last for $24$ days if $60$ more tonnes of steel is to be made that month.
View full question & answer→