MCQ 11 Mark
Rashmi types $510$ words in half an hour. How many words would she type in $10$ minutes$?$
AnswerLet $x$ be the number of words typed by Rashmi in $10$ minutes.
|
No. of words
|
$510$
|
$xx$
|
|
Time(in min)
|
$30$
|
$10$
|
Less time will be taken to type less number of words.
So, it is a case of direct variation.
Now, $\frac{510}{30}=\frac{\text{x}}{10}$
$⇒ x = 170$
$\therefore$ Rashmi will type $170$ words in $10$ minutes. View full question & answer→MCQ 21 Mark
Tick $(\checkmark)$ the correct answer in the folllowing: A car is travelling at a uniform speed of $75\ km/hr.$ How much distance will it cover in $20$ minutes$?$
- ✓
$25\ km$
- B
$15\ km$
- C
$30\ km$
- D
$20\ km$
AnswerCorrect option: A. $25\ km$
Let $x\ km$ be the required distance. Now, $1h = 60\ min$
| Distance (in km) |
$75$ |
$x$ |
| Time (in min) |
$60$ |
$20$ |
Less distance will be covered in less time.
Now, $\frac{75}{60}=\frac{\text{x}}{20}$
$\Rightarrow\text{x}=\frac{75\times20}{60}$
$\Rightarrow\text{x}=25\text{km}$ View full question & answer→MCQ 31 Mark
Tick $(\checkmark)$ the correct answer in the folllowing: A photograph of a bacteria enlarged $50000$ times attains a length of $5\ cm.$ The actual length of bacteria is:
- A
$ 1000 \mathrm{~cm} $
- B
$ 10^{-3} \mathrm{~cm} $
- ✓
$ 10^{-4} \mathrm{~cm} $
- D
$ 0^{-2} \mathrm{~cm} $
AnswerCorrect option: C. $ 10^{-4} \mathrm{~cm} $
Let $x\ cm$ be the actual length of the bacteria.
The larger the object, the larger its image will be.
Now, $\frac{\text{x}}{1}=\frac{5}{50000}=10^{-4}\text{cm}$
Hence, the actual length of the bacteria is $10^{-4} cm.$
View full question & answer→MCQ 41 Mark
$6$ pipes can fill a tank in $24$ minutes. One pipe can fill it in:
- A
$4$ minutes.
- B
$30$ minutes.
- C
$72$ minutes.
- ✓
$144$ minutes.
AnswerCorrect option: D. $144$ minutes.
Let one pipe take $x$ min to fill the tank.
|
No. of pipe
|
$6$
|
$1$
|
|
Time(in min)
|
$24$
|
$x$
|
Clearly, one pipe will take more time to fill the tank.
So, it is a case of inverse proportion.
Now, $6 × 24 = 1 × x$
$⇒ x = 6 × 24$
$⇒ x = 144$
$\therefore$ One pipe can fill the tank in $144$ minutes. View full question & answer→MCQ 51 Mark
$x$ and $y$ vary directly. When $x = 3,$ then $y = 36$. What will be the value of $x$ when $y = 96?$
Answer
| $xx$ |
$3$ |
$x_1$ |
| $yy$ |
$36$ |
$96$ |
$x$ and $y$ vary directly.
Then $x = ky,$ where $k$ is the constant of proportionality.
$\Rightarrow\text{K}=\frac{\text{x}}{\text{y}}$
Now, $\frac{3}{36}=\frac{\text{x}_1}{96}$
$\Rightarrow\frac{96\times3}{36}=\text{x}_1$
$\Rightarrow8=\text{x}_1$ View full question & answer→MCQ 61 Mark
Tick $(\checkmark)$ the correct answer in the folllowing: $3$ persons can build a wall in $4$ days, then $4$ persons can build it in.
- A
$5\frac{1}{3}$ days
- ✓
$3$ days
- C
$4\frac{1}{3}$days
- D
AnswerCorrect option: B. $3$ days
Let $x$ be number of days taken by $4$ persons to build the wall.
| No. of persons |
$3$ |
$4$ |
| No. of days |
$4$ |
$x$ |
More number of persons will take less time to build the wall.
So, it is a case of inverse proportion.
Now, $3 × 4 = 4 × x$
$⇒ x = 3$
Therefore, $4$ persons can build the wall in $3$ days. View full question & answer→MCQ 71 Mark
Tick $(\checkmark)$ the correct answer in the folllowing: If $8$ oranges cost $Rs. 52,$ how many oranges can be bought for $Rs. 169?$
AnswerLet the number of oranges that can be bought for $Rs. 169$ be $x.$
| Quantity(in kg) |
$8$ |
$x$ |
| Price(in Rs.) |
$52$ |
$169$ |
As the quantity increases the price also increases. So, this is a case of direct proportion.
$\therefore\frac{8}{52}=\frac{\text{x}}{169}$
$\Rightarrow\text{x}=\frac{8\times169}{52}=26$
Thus, $26$ oranges can be bought for $Rs. 169$ View full question & answer→MCQ 81 Mark
Tick $(\checkmark)$ the correct answer in the folllowing. $6$ pipes fill a tank in $120$ minutes, then $5$ pipes will fill it in.
- A
$100\ min$
- ✓
$144\ min$
- C
$140\ min$
- D
$108\ min$
AnswerCorrect option: B. $144\ min$
Let $x$ min be the time taken by $5$ pipes to fill the tank.
| No. of pipes |
$6$ |
$x$ |
| Time (in min) |
$10$ |
$7$ |
Less distance will be covered in less time.
Now, $6 × 120 = 5 × x$
$⇒ x = 144$
Therefore, $5$ pipes will take $144\ min$ to fill the tank. View full question & answer→MCQ 91 Mark
Tick $(\checkmark)$ the correct answer in the folllowing: A pole $14m$ high casts a shadow of $10m.$ At the same time, what will be the height of a tree, the length of whose shadow is $7$ metres$?$
AnswerCorrect option: B. $9.8m$
Let $x\ m$ be the height of the tree
| Height of object |
$14$ |
$x$ |
| Length of shadow |
$10$ |
$7$ |
Less distance will be covered in less time.
Now, $\frac{14}{10}=\frac{\text{x}}{7}$
$\Rightarrow\text{x}=\frac{14\times7}{10}$
$\Rightarrow\text{x}=9.8$
Therefore, a $9.8m$ tall tree will cast a shadow of length $7m.$ View full question & answer→MCQ 101 Mark
A car is travelling at an average speed of 60km per hour. How much distance will it cover in $1$ hour $12$ minutes$?$
- A
$50\ km$
- ✓
$72\ km$
- C
$63\ km$
- D
$67.2\ km$
AnswerCorrect option: B. $72\ km$
Let $x\ km$ be the distance covered in $1h\ 12\ min.$
Now, $1h\ 12\ min = (60 + 12)\ min = 72\ min.$
| Distance(in km) |
$60$ |
$xx$ |
| Time(in min) |
$60$ |
$72$ |
More distance will be covered in more time.
So, it is a case of direct proportion.
Now, $\frac{60}{60}=\frac{\text{x}}{72}$
$\Rightarrow\text{x} = 72\text{km}$
$\therefore$ The car will cover a distance of $72\ km$ in $1h\ 12\ min.$ View full question & answer→MCQ 111 Mark
Tick $(\checkmark)$ the correct answer in the folllowing: A machine fills $420$ bottles in $3$ hours. How many bottles will it fill in $5$ hours$?$
AnswerLet $x$ be the number of bottles filled in $5$ hours.
| No. of bottles |
$420$ |
$x$ |
| Time $(h)$ |
$3$ |
$5$ |
More number of bottles will be filled in more time.
Now, $\frac{420}{3}=\frac{\text{x}}{5}$
$\Rightarrow\text{x}=\frac{420\times5}{3}$
$\Rightarrow\text{x}=7$
Therefore, $700$ bottles would be filled in $5h.$ View full question & answer→MCQ 121 Mark
$35$ men can reap a field in $8$ days. In how many days can $20$ men reap it$?$
- ✓
$14$ days.
- B
$28$ days.
- C
$87\frac{1}{2}.$
- D
AnswerCorrect option: A. $14$ days.
Let $20$ men take $x$ days to reap the field.
| No. of days |
$8$ |
$xx$ |
| No. of men |
$35$ |
$20$ |
Clearly, less number of men will take more days.
So, it is a case of inverse proportion.
Now, $8 × 35 = x × 20$
$\Rightarrow\text{x}=\frac{8\times35}{20}$
$\Rightarrow\text{x} = 14$
$\therefore 20$ men can reap the field in $14$ days. View full question & answer→MCQ 131 Mark
Tick $(\checkmark)$ the correct answer in the folllowing: A car takes $2$ hours to reach a destination by travelling at $60\ km/hr.$ How long will it take while travelling at $80\ km/hr$
- ✓
$1\ hr\ 30\ min$
- B
$1hr \ 40\ min$
- C
$2\ hrs \ 40\ min$
- D
AnswerCorrect option: A. $1\ hr\ 30\ min$
Let $x\ h$ be the time taken by the car travelling at $80\ km/hr.$
| Speed (km/h) |
$60$ |
$80$ |
| Time (in h) |
$2$ |
$x$ |
The greater the speed, the lesser will be the time taken.
So, it is a case of inverse proportion.
Now, $60 × 2 = 80 × x$
$⇒ x = 12080$
$⇒ x = 1.5$
Therefore, the car will take $1h\ 30\ min$ to reach its destination if it travelsat a speed of $80\ km.$ View full question & answer→MCQ 141 Mark
Tick $(\checkmark)$ the correct answer in the folllowing: If $14\ kg$ of pulses cost $Rs. 882,$ what is the cost of $22\ kg$ of pulses$?$
- A
$Rs. 1254$
- B
$Rs. 1298$
- C
$Rs. 1342$
- ✓
$Rs. 1386$
AnswerCorrect option: D. $Rs. 1386$
Let $22\ kg$ of pulses cost $Rs. x$
| Quantity(in kg) |
$14$ |
$22$ |
| Price(in Rs.) |
$882$ |
$x$ |
As the quantity increases, the price also increases. So, it is a case of direct proportion.
$\therefore\frac{14}{882}=\frac{22}{\text{x}}$
$\Rightarrow\text{x}=\frac{22\times882}{14}=1386$
Thus the cost of $22\ kg$ of pilses is $Rs. 1,386$ View full question & answer→MCQ 151 Mark
$x$ and $y$ vary inversely. When $x = 15,$ then $y = 6.$ What will be the value of $y$ when $x = 9?$
Answer
| $x$ |
$15$
|
$9$
|
| $y$ |
$6$
|
$y_1$
|
Since $x$ and $y$ vary inversely, $xy =$ constant.
Now, $15 \times 6 = 9 \times y_1$
$\Rightarrow\frac{90}{9}=\text{y}_1$
$\Rightarrow10 = \text{y}_1$
$\therefore$ Value of $y = 10,$ when $x = 9.$ View full question & answer→MCQ 161 Mark
$14 $workers can build a wall in $42$ days. One worker can build it in:
- A
$3$ days.
- B
$147$ days.
- C
$294$ days.
- ✓
$588$ days.
AnswerCorrect option: D. $588$ days.
Let one worker take $x$ days to build the wall.
| No. of workers |
$14$ |
$1$ |
| No. of days |
$42$ |
$xx$ |
Clearly, one worker will take more days to finish the work.
So, it is a case of inverse proportion.
Now, $14 × 42 = 1 × x$
$⇒ x = 14 × 42$
$⇒ x = 588$
$\therefore$ One worker can build the wall in $588$ days. View full question & answer→MCQ 171 Mark
Tick $(\checkmark)$ the correct answer in the folllowing: The weight of $12$ sheets of a thick paper is $40$ grams. How many sheets would weight $1\ kg?$
AnswerLet $x$ sheets weigh $1\ kg.$ Now, $1\ kg = 1000g$
| No. of sheets |
$12$ |
$x$ |
| Weight (in g) |
$40$ |
$1000$ |
Now, $\frac{12}{40}=\frac{\text{x}}{1000}$
$\Rightarrow\text{x}=\frac{12\times1000}{40}$
$\Rightarrow\text{x}=300$ View full question & answer→MCQ 181 Mark
A car takes 2 hours to reach a destination by travelling at $60 km / hr$. How long will it take while travelling at $80 km / hr$ ?
View full question & answer→MCQ 191 Mark
3 persons can build a wall in 4 days, then 4 persons can build it in
- A
$5 \frac{1}{3}$ days
- ✓
- C
$4 \frac{1}{3}$ days
- D
View full question & answer→MCQ 201 Mark
6 pipes fill a tank in 120 minutes, then 5 pipes will fill it in
MCQ 211 Mark
A photograph of a bacteria enlarged 50000 times attains a length of 5 cm . The actual length of bacteria is?
Hint. Let the actual length be $x cm$. Then, $x \times 50000=5$.
$\therefore x=\frac{1}{10000}=\frac{1}{10^4}=10^{-4}$
- A
- B
$10^{-3} cm$
- ✓
$10^{-4} cm$
- D
$10^{-2} cm$
AnswerCorrect option: C. $10^{-4} cm$
View full question & answer→MCQ 221 Mark
A pole 14 m high casts a shadow of 10 m . At the same time, what will be the height of a tree the length of whose shadow is 7 metres?
MCQ 231 Mark
The weight of 12 sheets of a thick paper is 40 grams. How many sheets would weigh 1 kg ?
MCQ 241 Mark
A car is travelling at a uniform speed of 75 km / hr. How much distance will it cover in 20 minutes?
MCQ 251 Mark
A machine fills 420 bottles in 3 hours. How many bottles will it fill in 5 hours?
MCQ 261 Mark
If 8 oranges cost ₹ 52, how many oranges can be bought for $₹ 169$ ?
View full question & answer→MCQ 271 Mark
If 14 kg of pulses cost ₹ 882 , what is the cost of 22 kg of pulses?