MATHS M.C.Q. [1 Marks Each]

2. 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).

3. 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).

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).

4. 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).

2. 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).

2. 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).

4. 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).

3. 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).

2. 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).

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).

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).

2. 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.

2. 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).

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.