The number of teeth and the age of a person vary
- Adirectly with each other
- Binversely with each other
- Cneither directly nor inversely with each other
- ✓sometimes directly and sometimes inversely with each other
Answer: D.
View full solution →Question types
Direct & Inverse Proportion question types
87 questions across 11 question groups — pick any mix to generate a MATHS paper with step-by-step answer keys.
87
Questions
11
Question groups
5
Question types
01
M.C.Q. [1 Marks Each]
15 Q→02TRUE-FLASE [1 Marks Each]
5 Q→03Assertion (A) & Reason (B) MCQ
3 Q→042 Marks Questions
11 Q→053 Marks Question
25 Q→065 Marks Questions
2 Q→07Case study (4 Marks)
2 Q→08MATCH THE FOLLOWING.
1 Q→091 Marks Question
6 Q→10BLANKS [1 Marks Each]
5 Q→114 Mark Question
12 Q→Sample Questions
Direct & Inverse Proportion questions
One sample from each question group in this chapter. Select any group above to see the full set with answer keys.
If two quantities $p$ and $q$ vary inversely with each other, then
- A$\frac{p}{q}$ remains constant
- B$p+q$ remains constant
- ✓$p \times q$ remains constant
- D$p-q$ remains constant
Answer: C.
View full solution →Both $x$ and $y$ are in direct proportion, then $\frac{1}{x}$ and $\frac{1}{y}$ are
- ✓in direct proportion
- Bin inverse proportion
- Cneither in direct nor in inverse proportion
- Dsometimes in direct and sometimes in inverse proportion
Answer: A.
View full solution →In which of the following cases, $x$ and $y$ vary inversely as each other?
(i) Time taken to travel a given distance if speed changes
(ii) The number of people and time taken to complete a work
(iii) The length of a journey and the price of the ticket
(i) Time taken to travel a given distance if speed changes
(ii) The number of people and time taken to complete a work
(iii) The length of a journey and the price of the ticket
- AOnly (i)
- BOnly (ii)
- COnly (iii)
- ✓(i) and (ii)
Answer: D.
View full solution →Both $u$ and $v$ vary directly with each other. When $u$ is $10, v$ is 15 , which of the following is not a possible pair of corresponding values of $u$ and $v$ ?
- ✓15 and 20
- B2 and 3
- C25 and 37.5
- D16 and 24
Answer: A.
View full solution →When the speed is kept fixed, time and distance vary directly with each other.
If $x$ varies inversely as $y$ and when $x=6, y=8$, then for $x=8$ the value of $y$ is 10 .
View full solution →When two quantities $x$ and $y$ are in inverse proportion. then $\frac{x}{y}$ is a constant.
View full solution →If $p$ and $q$ are in inverse proportion, then $(p+2)$ and $(q-2)$ are also in inverse proportion.
View full solution →The distance travelled by CNG bus and the amount of CNG used are Inversely proportional.
Assertion (A) If $x$ varies directly as $y$ and $x=80$ when $y$ is 160 , then $y=128$, when $x=64$.
Reason (R) If $x$ varies directly as $y$, then $x y=k$, where $k$ is constant.
Reason (R) If $x$ varies directly as $y$, then $x y=k$, where $k$ is constant.
- ABoth A and R are true but R is the correct explanation of A
- BBoth A and R are true but R is not the correct explanation of A
- ✓A is true but R is false
- DA is false but R is true
Answer: C.
View full solution →Assertion (A) If you increase the number of workers on a project, then the time it takes to complete the project decreases.
Reason (R) The number of workers and the time to complete a project are directly proportional.
Reason (R) The number of workers and the time to complete a project are directly proportional.
- ABoth A and R are true but R is the correct explanation of A
- BBoth A and R are true but R is not the correct explanation of A
- ✓A is true but R is false
- DA is false but R is true
Answer: C.
View full solution →Assertion (A) When the speed of a car doubles, the time it takes to travel a certain distance is halved.
Reason (R) Speed and time are inversely proportion to each other.
Reason (R) Speed and time are inversely proportion to each other.
- ✓Both A and R are true but R is the correct explanation of A
- BBoth A and R are true but R is not the correct explanation of A
- CA is true but R is false
- DA is false but R is true
Answer: A.
View full solution →Which of the following are in inverse proportion?
The number of workers on a job and the time to complete the job.
The number of workers on a job and the time to complete the job.
A loaded truck travels 14 km in 25 min . If the speed remains the same, how far can it travel in 5h?
Suppose 2 kg of sugar contains $9 \times 10^6$ crystals. How many sugar crystals are there in
(i) 5 kg of sugar? $\qquad$ (ii) 1.2 kg of sugar?
View full solution →(i) 5 kg of sugar? $\qquad$ (ii) 1.2 kg of sugar?
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 would be its enlarged length?
In question 2 above, if 1 part of a red pigment requires 75 mL of base, how much red pigment should we mix with 1800 mL of base?
Observe the following tables and find which pair of variables (here, $x$ and $y$ ) are in inverse proportion?
(i)
(ii)
(iii)
View full solution →(i)
| x | 50 | 40 | 30 | 20 |
| y | 5 | 6 | 7 | 8 |
| x | 100 | 200 | 300 | 400 |
| y | 60 | 30 | 20 | 15 |
| x | 90 | 60 | 45 | 30 | 20 | 5 |
| y | 10 | 15 | 20 | 25 | 30 | 35 |
If we fix time period and the rate of interest, simple interest changes proportionally with principal. Would there be a similar relationship for compound interest? Why?
observe the following tables and find, if $x$ and $y$ are directly proportional.
View full solution →| x | 20 | 17 | 14 | 11 | 8 | 5 | 2 |
| y | 40 | 34 | 28 | 22 | 16 | 10 | 4 |
A school has 8 perlods in a day, each of 45 min duration. How long would each period be if the school has 9 periods, a day, assuming the number of school hours to be the same?
A car takes 2 h 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 →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:
(i) Are the number of spokes and the angles formed between the pairs of consecutive spokes in inverse proportion?
(ii) Calculate the angle between a pair of consecutive spokes on a wheel with 15 spokes.
(iii) How many spokes would be needed, if the angle between a pair of consecutive spokes is $40^{\circ}$ ?
View full solution →| Number of spokes | 4 | 6 | 8 | 10 | 12 |
| Angle between a pair of consecutive spokes | $90^{\circ}$ | $60^{\circ}$ | … | … | … |
(ii) Calculate the angle between a pair of consecutive spokes on a wheel with 15 spokes.
(iii) How many spokes would be needed, if the angle between a pair of consecutive spokes is $40^{\circ}$ ?
In a television game show, the prize money of ₹ 100000 is to be divided equally amongst the winners. Complete the following table and find whether the prize money given to an individual winner is directly or inversely proportional to the number of winners?
| Number of winners | Prize for each winner (in ₹) |
| 1 | 100000 |
| 2 | 50000 |
| 4 | … |
| 5 | … |
| 8 | … |
| 10 | … |
| 20 | … |
A hotel has 320 rooms and 32 cleaners to maintain them. With full capacity of staff, it took 2 h to clean all the rooms.
(i) On Monday 20% of the cleaners were not available. Will the cleaning of all rooms takes more time? How can you say so?
(ii) Ishan says, "The number of cleaners available in the hotel is directly proportional to the time taken by them to clean the rooms."
Mira says, "The number of clearners available in the hotel is inversely proportional to the time taken by them to clean the rooms."
Who is correct? Given reason.
(iii) Equal number of rooms are allocated for each staff member for cleaning. How many rooms each cleaner had to maintain?
(iv) The hotel administration hired 8 more cleaners. What is the change in number of rooms maintained by each cleaner?
(a) The total number of room increases by 2
(b) The total number of room decreases by 2
(c) The total number of room increases by 3
(d) The total number of room decreases by 3
(i) On Monday 20% of the cleaners were not available. Will the cleaning of all rooms takes more time? How can you say so?
(ii) Ishan says, "The number of cleaners available in the hotel is directly proportional to the time taken by them to clean the rooms."
Mira says, "The number of clearners available in the hotel is inversely proportional to the time taken by them to clean the rooms."
Who is correct? Given reason.
(iii) Equal number of rooms are allocated for each staff member for cleaning. How many rooms each cleaner had to maintain?
(iv) The hotel administration hired 8 more cleaners. What is the change in number of rooms maintained by each cleaner?
(a) The total number of room increases by 2
(b) The total number of room decreases by 2
(c) The total number of room increases by 3
(d) The total number of room decreases by 3
Deepak and his family went on a road trip by car. They visited four cities. City 1 was 500 km from their home. The petrol tank in their car has a capacity of 35 litres. The car runs 20 km on one litre.
From City 4, they travelled 500 km to reach home.
(i) How many litres of petrol did they use to complete the road trip?
(a) 100 $\qquad$ (b) 125 $\qquad$ (c) 200 $\qquad$ (d) 2500
(ii) The family travelled 500 km In a day. What is the smallest number of days in which the road trip can be completed?
(iii) The car travelled at a uniform speed of $75 km / h$ between City 3 and City 4 . How much distance did car travel in 20 min ?
(iv) The family started their journey from City 3 at 10 am . By what time will they reach half the distance to City 4 ?
(a) 12 pm $\qquad$ (b) 1:30 pm $\qquad$ (c) 1:20 pm $\qquad$ (d) 3 pm
View full solution →| City 1 | City 2 | City 3 | City 4 | |
| Distance travelled by the car | 500 | 1000 | 1500 | 2000 |
(i) How many litres of petrol did they use to complete the road trip?
(a) 100 $\qquad$ (b) 125 $\qquad$ (c) 200 $\qquad$ (d) 2500
(ii) The family travelled 500 km In a day. What is the smallest number of days in which the road trip can be completed?
(iii) The car travelled at a uniform speed of $75 km / h$ between City 3 and City 4 . How much distance did car travel in 20 min ?
(iv) The family started their journey from City 3 at 10 am . By what time will they reach half the distance to City 4 ?
(a) 12 pm $\qquad$ (b) 1:30 pm $\qquad$ (c) 1:20 pm $\qquad$ (d) 3 pm
| Column A | Column B |
| (i) $p$ and $q$ vary inversely to each other i.e. | (a) $p \propto q$ |
| (ii) Mathematical representation of direct variation of quantities m and n is | (b) $\frac{x}{y}=$ constant |
| (iii) When $x=5,y=2.5$ and when $y=5,x=10$ | (c) $m \propto n$ |
| (iv) If $x$ and $y$ vary directly, then on decreasing $x$, | (d) $x$ and $y$ are inversely proportional |
| (e) $p \propto \frac{1}{q}$ | |
| (f) $y$ will decrease in proportion |
observe the following tables and find, if $x$ and $y$ are directly proportional.
View full solution →| x | 5 | 8 | 12 | 15 | 18 | 20 |
| y | 15 | 24 | 36 | 60 | 72 | 100 |
observe the following tables and find, if $x$ and $y$ are directly proportional.
View full solution →| x | 6 | 10 | 14 | 18 | 22 | 26 | 30 |
| y | 4 | 8 | 12 | 16 | 20 | 24 | 28 |
Which of the following are in inverse proportion?
The population of a country and the area of land per person.
The population of a country and the area of land per person.
Which of the following are in inverse proportion?
The time taken for a fixed journey and the speed of the vehicle.
The time taken for a fixed journey and the speed of the vehicle.
Which of the following are in inverse proportion?
Area of cultivated land and the crop harvested.
Area of cultivated land and the crop harvested.
If the thickness of a pile of 12 cardboard sheets is 45 mm , then the thickness of a pile of 240 sheets is _________ cm .
Two quantities are said to vary _________ with each other if an increase in one causes, then a decrease in the other in such a manner that the product of their corresponding values remains constant.
When the speed remains constant, the distance travelled is _________ proportional to the time.
Let $x$ varies directly as $y^2$, for $y=3, x=2$. If $y=5$, then $x$ is _________
View full solution →$x$ and $y$ are said to vary directly with each other, if for some positive number $k$, _________ $=k$.
View full solution →Principal $=₹ 1000$, Rate $=8 \%$ per annum. Fill in the following table and find which type of interest (simple or compound) changes in direct proportion with time period.
View full solution →| Time period | 1 yr | 2 yr | 3 yr |
| Simple interest (in ₹) | |||
| Compound interest (in ₹) |
Two persons could fit new windows in a house in 3 days.
(i) One of the persons fell ill before the work started. How long would the job take now ?
(ii) How many persons would be needed to fit the windows in one day?
(i) One of the persons fell ill before the work started. How long would the job take now ?
(ii) How many persons would be needed to fit the windows in one day?
A mixture of paint is prepared by mixing 1 part of red pigment with 8 parts of base. In the following table, find the parts of base that need to be added.
| Parts of red pigment | 1 | 4 | 7 | 12 | 20 |
| Parts of base | 8 | … | … | … | … |
The following table shows the distance travelled by one of the new eco-friendly energy efficient cars travelled on gas.
Which type of properties are indicated by the table? How much distance will be covered by the car in 8 L of gas?
| Litres of gas | 1 | 0.5 | 2 | 2.5 | 3 | 5 |
| Distance (km) | 15 | 7.5 | 30 | 37.5 | 45 | 75 |
Which type of properties are indicated by the table? How much distance will be covered by the car in 8 L of gas?
A volleyball court is in a rectangular shape and its dimensions are directly proportional to the dimensions of the swimming pool given below. Find the width of the pool.
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