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Maths 3 Mark Question

Unitary Method · Maharashtra Board STD 7 (MSBSHSE - English Medium). 20 questions.

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3 Mark Question

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Question 13 Marks
A train covers a distance of 51km in 45 minutes. How long will it take to cover 221km?
Answer
To cover a distance of 51km, time is taken = 45 minutes
$=\frac{3}{4}$ hours
To cover a distance of 1km, time will be
Taken $=\frac{3}{4\times51}$ hours
And to cover a distance of 221km 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.
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Question 23 Marks
If 22.5 metres of a uniform iron rod weighs 85.5kg, what will be the length of 22.8kg of the same rod?
Answer
If weight is 85.5kg, then length of iron rod = 22.5m
If weight is 1kg, then length of rod will be
$=\frac{22.5}{85.5}\text{m}$
And if weight is 22,8kg, then length of rod will be
$=\frac{22.5\times22.8}{85.5}\text{m}$
$=\frac{225\times228\times10}{10\times855\times10}\text{m}$
$=\frac{45\times228}{2\times855}\text{m}$
$=\frac{1\times114}{1\times19}=6\text{m}$
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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?
Answer
Time taken to type 40 words per minute = 24 min
Time taken to type a word per minute = 24 × 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.
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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?
Answer
Days 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.
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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.
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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?
Answer
If 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
$=\frac{7}{8.2}\times20.5=\frac{7\times5}{2}$
$=\frac{35}{2}\text{m}=17.5\text{m}$
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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.
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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?
Answer
Time taken to cover the distance at a speed of 45 km/ h = 3h 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.
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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?
Answer
No. of men required to reap the field in 30 days = 16
No. of men required to reap the field in 1 day = 16 × 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.
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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 $=\frac{15\times26}{16.25}$
$=\frac{15\times26\times100}{1625}=3\times2\times4=24\text{ men}$
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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?
Answer
Number of days for which the food is sufficient for 120 men = 195
Number of days for which food is sufficient for 1 man = 120 × 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.
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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.
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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 13.5kg?
Answer
In 162 grams, sheets are = 6
In 1gm sheets will be $=\frac{6}{162}$
And in 13.5kg or 13500gms, sheets will be
$=\frac{6\times13500}{162}$
$=\frac{1\times13500}{27}=500$ sheets.
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Question 143 Marks
45 cows can graze a field in 13 days. How many cows will graze the same field in 9 days?
Answer
Number 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.
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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?
Answer
Initially, 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.
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Question 163 Marks
If the thickness of a pile of 16 cardboards is 44mm how many cardboards will be there in a pile which is 71.5cm thick?
Answer
In 44 mm of thickness, cardboards are = 16
In 1mm of thickness, cardboards will be
$=\frac{16}{44}$
And in 71.5cm or 7.15mm cardboards will be
$=\frac{16\times715}{44}=\frac{4\times715}{11}=4\times65$
260 cardboards.
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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?
Answer
Time taken by 16 horses to consume the corn = 25 days
Time taken by 1 horse to consume the corn = 25 × 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.
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Question 183 Marks
The extension of an elastic string varies directly as the weight hung on it. If a weight of 150g produces an extension of 2.8cm, what weight would produce an extension of. 19.6cm?
Answer
2.8cm extension is produced by = 150g.
1cm extension will be produced by $=\frac{150}{2.8}\text{g}$
and 19.6cm extension will be produced by
$=\frac{150\times19.6}{2.8}\text{g}=\frac{150\times196\times10}{10\times28}\text{g}$
$=\frac{150\times196}{28}=150\times7\text{g}$
$=1\text{kg }50\text{g.}$
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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?
Answer
No. 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.
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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?
Answer
Time taken to make 240 tonnes of steel = 30 days
Time taken to make 1 tonne of steel = 30 × 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.
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