Application of Inverse Proportionality

Q. Question 11.
A school has 8 periods a day each of 45 minutes 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?

Q.

Three pot have the same volume . The ratio of the milk and water in first, second and third pots are 3:2, 7:3 and 11:4 respectively. If the liquids of the three are mixed, then find the ratio of milk and water .

Q.

Question 94

A Water tank casts a shadow 21 m long. A tree of height 9.5 m caste a shadow 8 m long at the same time. The length of the shadows are directly proportional to their heights. Find the height of the tank.

Q. 39 men can build a bridge in 12 days, working 5 hours a day. In how many days will 30 men, working 6 hours a day, complete the work?

1. 10
2. 13
3. 14
4. 15

Q.

In which of the following equations is x and y in inverse proportion ?

1. xy = 6

2. y = x+3

3. $\frac{y}{4}=x$

4. x= y-2

Q.

In a school, there are 8 periods per day each of 1 hour duration. How long would each period be, if 4 more periods are to be added, assuming the number of school hours to be same? [2 MARKS]

Q. Ipsa bought a car which covers 363 km in 24.2 litres of petrol. What will be the distance covered using 7 litres of petrol?

1. 213 km
2. 67 km
3. 105 km
4. 86 km

Q. A gardener uses pipes to water his garden from a tank. He uses 6 pipes to do it and it takes 1 hour 20 minutes to completely empty the tank. Now, if he uses only 5 pipes to water the garden, how long will it take to empty the tank?

1. 1 hour 30 mins
2. 1 hour 36 mins
3. 1 hour 55 mins
4. 1 hour 45 mins

Q. No. of people required to complete a work and time required for the same are in proportion.

1. direct
2. continued
3. inverse

Q.

Esha travelled $2.15\mathrm{km}$ by walking, $5.75\mathrm{km}$ by a bus and then $30.25\mathrm{km}$ by a local train. Find the total distance travelled in metres.

Q.

A fixed volume of water flows into a rectangular water tank such that the rate of water flow can be changed by using different pipes. Which of the following relations represent(s) inverse proportions?

1. The number of pipes used and the amount of water flow into the tank

2. The volume of the pipe used and time taken to fill the tank.

3. The rate of water flow and the time taken to fill the tank

4. The rate of water flow and the height of the water level.

Q.

Given that x and y are in direct proportion, and $y_1,y_2$ are values of $y$ corresponding to the values $x_1,x_2$ of $x$ respectively. Which of the following is correct?

1. $x_1{y}_2=x_2{y}_1$
2. $x_1{y}_1=x_2{y}_2$
3. $x_1{x}_2=y_1{y}_2$
4. $\frac{x_1}{y_1}$ = $\frac{y_2}{x_2}$

Q.

A raft was sent away from point $\mathrm{A}$ downstream.

A patrol boat left $\mathrm{A}$ $5$ hour and $20$ min later and caught up with the raft $20\mathrm{km}$ away from point $\mathrm{A}$.

What was the speed of the raft if the speed of the patrol-boat was $12\mathrm{km}/\mathrm{hour}$?

Q.

Determine if the following are in proportion: $15,45,40,120$

Q. A sum of money is to be distributed among A, B, C and D in the proportion of 5 :2 :: 4 : 3. If C gets Rs. 1000 more than D, what is B's share ?

1. 1000
2. 2000
3. 3000
4. 4000

Q.

Question 01.
Which of the following are in inverse proportion?
(i) The number of workers on a job and the time to complete the job.
(ii) The time taken for a journey and the distance travelled in a uniform speed.
(iii) Area of cultivated land and the crop harvested.
(iv) The time taken for a fixed journey and the speed of the vehicle.
(v) The population of a country and the area of land per person.

Q. If a teacher has a fixed number of toffees, then number of students and toffees they get after distributing equally are in proportion.

1. direct
2. inverse
3. continued

Q. $36$ men can construct a bridge in $18$ days. In how many days will $27$ men complete the construction?

1. $12$
2. $18$
3. $22$
4. $24$

Q.

Determine if the following are in proportion: $33,44,75,100$

Q.

Determine if the following are in proportion: $24,28,36,48$

Q.

Determine if the following are in proportion $33,121,9,96$

Q.

A farmer has enough food to feed 20 cattle for 6 days. The number of days food will last if there were 10 more cattle is

___

Q.

Madan walked $12.65$km on Monday, $13.04$km on Tuesday, and $11.96$km on Wednesday. How much distance did he walk in all?

Q.

Question 100

The variable x is inversely proportional to y. If x increase by P%, then by what per cent will y decrease?