Sample QuestionsDirect and Inverse Proportions questions
One sample from each question group in this chapter. Select any group above to see the full set with answer keys.
$11$ musicians create a song in $3$ days. How many days would be required to create a song when 6 musicians are working together'?
Answer: C.
View full solution →Both $x$ and $y$ are in direct proportion, then$\frac{1}{\text{x}}$ and $\frac{1}{\text{y}}$ are:
- A
- ✓
- C
Neither in direct nor in inverse proportion.
- D
Sometimes in direct and sometimes in inverse proportion.
Answer: B.
View full solution →A train travels $60\ km$ in $1$ hour. How long will it take to go $150\ km?$
- A
$2$ hours
- B
$3$ hours
- ✓
$2.5$ hours
- D
$4$ hours
Answer: C.
View full solution →If $20$ cows eat as much as $15$ oxen, how many cows will eat at much as $36$ oxen?
Answer: D.
View full solution →If $12$ workers can build a wall in $50$ hours, how many workers will be required to do the same work in $40$ hours?
Answer: D.
View full solution →Directions: In the following questions, the Assertions $(A)$ and Reason(s) $(R)$ have been put forward. Read both the statements carefully and choose the correct alternative from the following:
Assertion (A): Apala types $200$ words in half an hour. Then she will type $90$ words in $12$ minutes
Reasons (R): A direct proportion shows the direct the relation between two quantities. An inverse proportion shows inverse or indirect relation between two quantities
- A
Both $A$ and $R$ are true and $R$ is the correct explanation of $A$.
- B
Both $A$ and $R$ are true but $R$ is not the correct explanation of $A$.
- C
$A$ is true but $R$ is false.
- ✓
$A$ is false but $R$ is true.
Answer: D.
View full solution →Directions: In the following questions, the Assertions $(A)$ and Reason(s) $(R)$ have been put forward. Read both the statements carefully and choose the correct alternative from the following:
Assertion (A): $20$ trucks can hold $150$ metric tonnes. $12$ trucks will hold $80$ metric tonnes. Reasons
(R): A direct proportion shows the direct the relation between two quantities.
- A
Both $A$ and $R$ are true and $R$ is the correct explanation of $A$.
- B
Both $A$ and $R$ are true but $R$ is not the correct explanation of $A$.
- C
$A$ is true but $R$ is false.
- ✓
$A$ is false but $R$ is true.
Answer: D.
View full solution →Directions: In the following questions, the Assertions $(A)$ and Reason(s) $(R)$ have been put forward. Read both the statements carefully and choose the correct alternative from the following:
Assertion (A): The rent of $7$ hectares is $Rs 875. 16$ hectares = Rs $1600$
Reasons (R): A direct proportion shows the direct the relation between two quantities.
- A
Both $A$ and $R$ are true and $R$ is the correct explanation of $A$.
- B
Both $A$ and $R$ are true but $R$ is not the correct explanation of $A$.
- C
$A$ is true but $R$ is false.
- ✓
$A$ is false but $R$ is true.
Answer: D.
View full solution →Directions: In the following questions, the Assertions $(A)$ and Reason(s) $(R)$ have been put forward. Read both the statements carefully and choose the correct alternative from the following: Assertion (A): A machine in a soft drink factory fills $600$ bottles in $5$ hours. Then $240$ bottles will it fill in $2$ hours Reasons (R): A direct proportion shows the direct the relation between two quantities. An inverse proportion shows inverse or indirect relation between two quantities
- ✓
Both $A$ and $R$ are true and $R$ is the correct explanation of $A$.
- B
Both $A$ and $R$ are true but $R$ is not the correct explanation of $A$.
- C
$A$ is true but $R$ is false.
- D
$A$ is false but $R$ is true.
Answer: A.
View full solution →Directions: In the following questions, the Assertions $(A)$ and Reason(s) $(R)$ have been put forward. Read both the statements carefully and choose the correct alternative from the following:
Assertion (A): A boy runs $1k\ m$ in $10$ minutes. Then He will take $6$ minutes to ran $600\ m$
Reasons (R): A direct proportion shows the direct the relation between two quantities.
- ✓
Both $A$ and $R$ are true and $R$ is the correct explanation of $A$.
- B
Both $A$ and $R$ are true but $R$ is not the correct explanation of $A$.
- C
$A$ is true but $R$ is false.
- D
$A$ is false but $R$ is true.
Answer: A.
View full solution →A car takes $2$ hours to reach a destination by travelling at the speed of $60\ km/h$. How long will it take when the car travels at the speed of $80\ km/h$?
View full solution →A factory requires $42$ machines to produce a given number of articles in $63$ days. How many machines would required to produce the same number of articles in $54$ days ?
View full solution →A batch of bottles were packed in $25$ boxes with $12$ bottles in each box. If the same batch is packed using $20$ bottles in each box, how many boxes would be filled?
View full solution →A contractor estimates that $3$ persons could rewire Jasminder's house in $4$ days. If, he uses $4$ persons instead of three, how long should they take to complete the job ?
View full solution →A farmer has enough food to feed $20$ animals in his cattle for 6 days. How long would the food last if there were 10 more animals in his cattle ?
View full solution →If a box of sweets is divided among $24$ children, they will get $5$ sweets each. How many would each get, if the number of the children is reduced by $4?$
View full solution →Rehman is making a wheel using spokes. He wants to fix equal spokes in such a way that the angles between any pair of consecutive spokes are equal. Help him by completing the following table.
.
| Numbers of spokes |
$4$ |
$6$ |
$8$ |
$10$ |
$12$ |
| Angle between a pair of consecutive spokes |
$90^\circ $ |
$60^\circ $ |
– |
– |
– |
How many spokes would be needed, if the angle between a pair of consecutive spokes is $40^\circ ?$ View full solution →Rehman is making a wheel using spokes. He wants to fix equal spokes in such a way that the angles between any pair of consecutive spokes are equal. Help him by completing the following table.
.
| Numbers of spokes |
$4$ |
$6$ |
$8$ |
$10$ |
$12$ |
| Angle between a pair of consecutive spokes |
$90^\circ $ |
$60^\circ $ |
– |
– |
– |
Calculate the angle between a pair of consecutive spokes on a wheel with $15$ spokes? View full solution →In a Television game show, the prize money of ₹$1,00,000$ is to be divided equally amongst the winners. Complete the table and find whether the prize money given to an individual winner is directly or inversely proportional to the number of winners:
| No. of winners |
$1$ |
$2$ |
$4$ |
$5$ |
$8$ |
$10$ |
$20$ |
| Prize for each winner (in ₹) |
$1,00,000$ |
$50,000$ |
... |
... |
... |
... |
... |
View full solution →Rashmi has a road map with a scale of $1 \ cm$ representing $18 \ km$. She drives on a road for $72 \ km$. What would be her distance covered in the map ?
View full solution →A 5 m 60 cm high vertical pole casts a shadow $3\ m$ $20\ cm$ long. Find at the same time the height of a pole which casts a shadow 5m long.
View full solution →A $5\ m$ $60\ cm$ high vertical pole casts a shadow $3\ m 20\ cm$ long. Find at the same time the length of the shadow cast by another pole $10\ m$ $50\ cm$ high.
View full solution →In a model of a ship, the mast is $9\ m$ high, while the mast of the actual ship is $12\ m$ high. If the length of the ship is $28\ m$, how long is the model ship?
View full solution →A photograph of a bacteria enlarged $50000$ times attains a length of $5\ cm$ as shown in the diagram. What is the actual length of the bacteria? If the photograph is enlarged $20000$ times only, what be its enlarged length?
View full solution →If $1$ part of a red pigment requires $75\ mL$ of base, how much red pigment should we mix with $1800\ mL$ of base ?
View full solution →Is the population of a country and the area of land per person are in inverse proportion ?
Is the time taken for a fixed journey and the speed of the vehicle in inverse proportion ?
Is the area of cultivated land and the crop harvested in inverse proportion ?
Is the time taken for a journey and the distance travelled in a uniform speed in inverse proportion ?
Is the number of workers on a job and the time to complete the job in inverse proportion ?
If $x$ varies inversely as $y,$ then
|
$x$
|
$-$
|
$60$
|
|
$y$
|
$2$
|
$10$
|
View full solution →If d varies directly as $t^2$, then we can write $dt^2= k$, where $k$ is some constant.
View full solution →Both $x$ and $y$ are said to vary _______ with each other if for some positive number $k, xy = k.$
View full solution →If $x$ and $y$ are in inverse proportion, then $(x + 1)$ and $(y + 1)$ are also in inverse proportion.
View full solution →On increasing $a, b$ increases in such a manner that $\frac{\text{a}}{\text{b}}$ remains _____ and positive, then $a$ and $b$ are said to vary directly with each other.
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