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Maths 1 Mark Question

Unitary Method · Maharashtra Board STD 7 (MSBSHSE - Semi English Medium). 14 questions.

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Question 11 Mark
What distance (in m) will a train cover in 1 minute travelling at $72\frac{\text{km}}{\text{h}}$?
  1. 120
  2. 1200
  3. 1400
  4. 720
Answer
  1. 1200
Solution:

As, the speed of the train $=72\frac{\text{km}}{\text{hr}}$

⇒ The distance covered in 1 hour (60 min) $=72\text{km}$

$\therefore$ The distance covered in 1 minute $=\frac{72}{60}\text{km}$

$=\frac{6}{5}\text{km}$

$=\frac{6}{5}\times1000\text{m}$

$=6\times200\text{m}$

$=1200\text{m}$

Hence, the correct alternative option (b).
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Question 21 Mark
If a person travels 150km in 5 hours, then the time taken by him to travel 180km is:
  1. 3 hours
  2. 4 hours
  3. 8 hours
  4. 6 hours
Answer
  1. 6 hours
Solution:

As, the time taken by the person to travel 150km = 5 hours

⇒ The time taken by him to travel 1km $=\frac{5}{150}=\frac{1}{30}\text{ hours}$

So, the time taken by him to travel 180km $=\frac{1}{30}\times180\text{ hours}=6 \text{ hours}$

Hence, the correct alternative is option (d).
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Question 31 Mark
The cost of 30 mangoes is less then cost of 40 mangoes by Rs. 50. Find the cost of 50 mangoes in (Rs.)
  1. 400
  2. 300
  3. 250
  4. 350
Answer
  1. 250
Solution:

As, the cost of 30 mangoes is less than the cost of 40 mangoes by Rs. 50

⇒ The cost of 10 mangoes = Rs. 50

⇒ The cost of 1 mango $=\frac{50}{10}=\text{Rs. }5$

So, the cost of 50 mangoes = 5 × 50 = Rs. 250

Hence, the correct alternative option (c).
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Question 41 Mark
If $\frac{4}{5}$ of a water tank is filled in 1 hour, then how much time will be required to fill the rest of it?
  1. 20 minutes
  2. 15 minutes
  3. 12 minutes
  4. 10 minutes
Answer
  1. 15 minutes
Solution:

As, the time taken to fill $\frac{4}{5}$ of the water tank = 1hr = 60min

⇒ The time taken to fill the water tank $=60\times\frac{5}{4}=15\times5=75\text{min}$

So, the time required to fill the rest of the water tank = 75 - 60 = 15min

Hence, the correct alternative is option (b).
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Question 51 Mark
If 6 bowls cost Rs. 90, then the cost of 10 such bowls is:
  1. Rs. 125
  2. Rs. 175
  3. Rs. 150
  4. Rs. 120
Answer
  1. Rs. 150
Solution:

As, the cost of 6 bowls = Rs. 90

⇒ The cost of 1 bowl $=\frac{90}{6}=\text{Rs. }15$

So, the cost of 10 bowls = 15 × 10 = Rs. 150

Hence, the correct alternative is option (c).
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Question 61 Mark
8 men can finish a piece of work in 40 days. If 2 more men join them, then the work will be computed in:
  1. 30 days
  2. 32 days
  3. 36 days
  4. 25 days
Answer
  1. 32 days
Solution:

As, the number of days computed by 8 men to finish the piece of work = 40 days

⇒ The number of days computed by 1 man to finish the piece of work = 40 × 8 = 320 days

So, the number of days computed by 10 men to finish the piece of work = $\frac{320}{10}=32\text{ days}$

Hence, the correct alternative is option (b).

Note: This is the case of inverse variation. More men needs less time to finish the same work.
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Question 71 Mark
If the cost of 15 mangoes is Rs. 180, then what is the cost of 25 mangoes?
  1. 220
  2. 360
  3. 200
  4. 300
Answer
  1. 300
Solution:

As, the cost of 15 mangoes = Rs. 180

⇒ The cost of 1 mango $=\frac{180}{15}=\text{Rs. }12$

So, the cost of 25 mangoes = 25 × 12 = Rs. 300

Hence, the correct alternative option (d).
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Question 81 Mark
6 dozen eggs are bought for Rs. 108. How much will 108 eggs cost?
  1. Rs. 171
  2. Rs. 162
  3. Rs. 153
  4. Rs. 180
Answer
  1. Rs. 162
Solution:

As, the cost of 6 dozen eggs (6 × 12 = 72 eggs) = Rs. 108

⇒ The cost of 1 egg $=\frac{108}{72}=\frac{3}{2}$

So, the cost of 108 eggs $=\frac{3}{2}\times108=3\times54=\text{Rs. }162$

Hence, the correct alternative is option (b).
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Question 91 Mark
A worker makes a toy every $\frac{2}{3}\text{hr}$. If he works for $7\frac{1}{3}\text{hr}$, then how many toys will he make?
  1. 11
  2. 16
  3. 18
  4. 22
Answer
  1. 11
Solution:

As, the number of toys made by the worker in $\frac{2}{3}\text{hr}=1$

⇒ The number of toys made by him in 1 hour $=1\times\frac{3}{2}=\frac{3}{2}$

So, the number of toys made by the worker in $7\frac{1}{3}\text{hr }\Big(\frac{22}{3}\Big)\text{hr}=\frac{3}{2}\times\frac{22}{3}=11$

Hence, the correct alternative is option (a).
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Question 101 Mark
If the cost of 12 books is Rs. 144, then the cost of 18 books is:
  1. Rs. 206
  2. Rs. 216
  3. Rs. 198
  4. Rs. 180
Answer
  1. Rs. 216
Solution:

As, the cost of 12 books = Rs. 144

⇒ The cost of 1 book $\frac{144}{12}=\text{Rs. }12$

So, the cost of 18 books = 12 × 18 = Rs. 216

Hence, the correct alternative is option (b).
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Question 111 Mark
If 21 cows eat as much as 15 buffaloes, then how many cows will eat as much as 35 buffaloes?
  1. 45
  2. 49
  3. 56
  4. 54
Answer
  1. 49
Solution:

As, the number of cows that eat as much as 15 buffaloes = 21

⇒ The number of cows that eat as much as 1 buffalo $=\frac{21}{15}=\frac{7}{5}$

So, the number of cows that eat as much as 35 buffaloes $=\frac{7}{5}\times35=7\times7=49$

Hence, the correct alternative is option (b).
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Question 121 Mark
A car can go 150km with 25 litres of petrol. How for can it go with 30 litres of petrol?
  1. 180
  2. 150
  3. 210
  4. 160
Answer
  1. 180
Solution:

As, the distance travelled by the car with 25 litres of petrol = 150km

⇒ The distance travelled by the car with 1 litre of petrol $\frac{150}{25}=6\text{km}$

So, the distance travelled by the car with 30 litres of petrol = 6 × 30 = 180km

Hence, the correct alternative is option (a).
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Question 131 Mark
If the cost of 25 pencils is Rs. 75, then the cost of 75 pencils is:
  1. 225
  2. 150
  3. 180
  4. 100
Answer
  1. 225
Solution:

As, the cost of 25 pencils = Rs. 75

⇒ The cost of 1 pencil $=\frac{75}{25}=\text{Rs. }3$

So, the cost of 75 pencils = 3 × 75 = Rs. 225

Hence, the correct alternative option (a).
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Question 141 Mark
45 cows can graze a field in 12 days. How many cows will graze the same field in 9 days?
  1. 60 cows
  2. $38\frac{3}{4}\text{ cows}$
  3. 54 cows
  4. 45 cows
Answer
  1. 60 cows
Solution:

As, the number of cows that can graze the field in 12 days = 45

⇒ The number of cows that can graze the field in 1 days = 45 × 12 = 540

So, the number of cows that can graze the field in 9 days $=\frac{540}{9}=60\text{ cows}$

Hence, the correct alternative is option (a).

Note: This is a situation of inverse variation. More the number of cows, the faster will they graze the field.

The options given in the book are incorrect. The same has been corrected here.
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