Inverse Proportion

Q. If $36$ men can complete a piece of work in $18$ days. In how many days will $27$ men complete the same amount of work ?

1. $24$
2. $36$
3. $30$
4. $12$

Q. $P$ and $Q$ can do a piece of work in 20 days and 30 days respectively. They started the work together and Q left after some days of work and P finished the remaining work in 5 days. After how many days from the start did Q leave?

Q.

x and y are in direct proportion if xy=constant

1. True

2. False

Q. If 80 people can finish a work within 16 days by labouring 6 hours a day. Then how many hours per day should 64 people work to complete that job within 15 days?

1. 8 hours
2. 5 hours
3. 10 hours
4. 15 hours

Q.

Observe the tables given below and in each one find whether x and y are proportional :

(i) $\begin{array}{cccccc}x& 3& 5& 8& 11& 26\\ y& 9& 15& 24& 33& 78\end{array}$

(ii) $\begin{array}{cccccc}x& 2.5& 4& 7.5& 10& 14\\ y& 10& 16& 30& 40& 42\end{array}$

(iii) $\begin{array}{ccccccc}x& 5& 7& 9& 15& 18& 25\\ y& 15& 21& 27& 60& 72& 75\end{array}$

Q.

If x and y vary inversely and x = 15 when y = 6, find y when x = 9.

Q. If 9 kg of sugar costs ₹ 238.50, how much sugar can be bought for ₹ 371?

Q.

In a triangle, if $r_1=2r_2=3r_3,$then $\frac{a}{b}+\frac{b}{c}+\frac{c}{a}$ is equal to:

1. $\frac{75}{60}$

2. $\frac{155}{60}$

3. $\frac{176}{60}$

4. $\frac{191}{60}$

Q.

When two ratios are equal in value, then they are said to be in proportion.

1. Partnership

2. Proportion

Q. 5 men can work together to finish a piece of work in 25 days. How many days will 20 men take to complete that same piece of work? [2 Marks]

Q.

If the rate of increase of the area of a circle is not constant but the rate of increase of perimeter is constant, then the rate of increase of area varies

1. As the square of the perimeter

2. Inversely as the perimeter

3. As the radius

4. Inversely as the radius

Q.

Pradeep receives an export order for garments. He has$30$ machines to complete the order in$60$ days. How many machines would be required to complete the job in$40$ days?

Q. If 81 students can do a painting on a wall of length $448m$ in 56 days, then how many students can do the painting on a similar type of wall of length $160m$ in 27 days?

Q. Which is example of inverse proportion?

1. Length of edge of square & its area
2. Length of edge of square & its perimeter
3. Speed and time taken
4. Quantity of pencils & total cost

Q.

Question 9

Which of the following vary inversely with each other?
(a) Speed and distance covered
(b) Distance covered and taxi fare
(c) Distance travelled and time taken
(d) Speed and time taken

Q. 2 men and 5 women can a piece of work in 4 days while one man and one woman can finish it in 12 days . how long would it take for 1 man to do work.

Q. Three people A, B and C can do a job alone in 10 days, 12 days and 15 days respectively. In how many days they can finish the job working together?

1. 4 days
2. $\frac{7}{2}$ days
3. 6 days
4. $2\frac{1}{3}$ days

Q. A taxi charges a fare of Rs 2550 for a journey of 150 km. How much would it charge for a journey of 124 km?

Q.

Question 55

When two quantities are related in such a manner that if one increases and the other decreases, then they always vary inversely.

Q.

Question 20

When two quantities x and y are in ___proportion or vary ___, they are written as $x\propto \frac{1}{y}$.

Q. 20 men can do a work in 5 days. How many days will 10 men take to complete that work?

1. 15 days
2. 11 days
3. 8 days
4. 10 days

Q. Seeds kept in a refrigerator do not germinate because _________.

1. they don't get enough air
2. all of the above
3. they don't get enough water
4. they don't get the optimum temperature

Q.

Question 60

In questions which of the following vary directly and which vary inversely with each other and which are neither of the two?
(i) The time taken by a train to cover a fixed distance and the speed of the train.
(ii) The disatnce travelled by CNG bus and the amount of CNG used.
(iii) The number of people working and the time to complete a given work.
(iv) Income tax and the income.
(v) Distance travelled by an auto-rickshaw and time taken.

Q.

Question 61

In questions which of the following vary directly and which vary inversely with each other and which are neither of the two?
(i) Number of students in a hostel and consumption of food.
(ii) Area of the walls of a room and the cost of whitewashing the walls.
(iii) The number of people working and the quantity of work.
(iv) Simple interest on a given sum and the rate of interest.
(v) Compound interest on a given sum and the sum invested.

Q.

Question 1 (vi)
Find the value of unknown x in the following diagrams.

Q. In a fort, 200 men had provision for 60 days. After 20 days, 40 men were shifted to other places. How long will the provision last for remaining men at the same rate?

1. 54 days
2. 50 days
3. 60 days
4. 55 days

Q.

Question 57

The number of workers and the time to complete a job is a case of direct proportion.

Q.

Question 62

In questions which of the following vary directly and which vary inversely with each other and which are neither of the two?
(i) The quantity of rice and its cost.
(ii) The height of a tree and the number of years.
(iii) Increase in cost and number of shirts that can be purchased, if the budget remains the same.
(iv) Area of land and its cost.
(v) Sales tax and the amount of the bill.

Q. If 28 men can do a piece of work in 7 days, then how many men are required to complete that work in 4 days?

1. 45 men
2. 42 men
3. 50 men
4. 49 men

Q. A work can be done by 32 men in 11 days. 10 of them did not join the work. How long will it take now to complete the work?

1. 15 days
2. 12 days
3. 16 days
4. 12 days