Inverse Proportion

Q. 39 persons can repair a road in 12 days, working 5 hours a day. In how many days will 30 persons working 6 hours a day complete the work. [4 MARKS]

Q.

What are real-life examples of inverse proportion?

Q.

If it takes $5$ machines $5$ minutes to make $5$ widgets, how long would it take $100$ machines to make $100$ widgets?

Q. 12 workers can build a house in 30 days. If 15 workers build the same house, how many days will they need?

1. 24
2. 15
3. 37.5
4. 48

Q. If 600 rupees buy 15 bunches of feed, how many will 1280 rupees buy?

Q. The cost of 12 quintals of soyabean is 36, 000 rupees. How much will 8 quintals cost?

Q. The stock of grain in a government warehouse lasts 30 days for 4000 people. How many days will it last for 6000 people ?

Q. With a speed of 60 km/h, a car takes 4 hours to cover a certain distance.
Enter the speed of the car in km/h, if the same distance has to be covered in 3 hours.

1. 80

Q. Two mobiles cost 16, 000 rupees. How much money will be required to buy 13 such mobiles ?

Q. If the change in one quantity produces a proportionate decrease or increase in another quantity such that their product is constant, then we say that the two quantities are in inverse variation. State whether the statement is True or False.

1. True
2. False

Q. If $x_1:y_1$ and $x_2:y_2$ are in inverse proportion, then:

1. $\frac{x_2}{x_1}=\frac{y_1}{y_2}$
2. $x_2\times y_1=x_1\times y_2$
3. $x_1\times y_1=x_2\times y_2$
4. $\frac{x_2}{y_2}=\frac{x_1}{y_1}$

Q.

If two cardboard boxes occupy $500$ cubic centimetres space, then ___ cubic centimetres space will be required to keep $200$ such boxes?

Q. If the cost of a book is ₹ 25.57, find the cost of 24 such books.

1. ₹746.58
2. ₹558.08
3. ₹613.68
4. ₹618.48

Q. If 8 workers can build a wall in 10 days then match the number of workers with the number of days.

1. 20 days
2. 40 days
3. 16 days
4. 8 days

Q.

If 3 people can weave 168 shawls in 14 days, how many shawls will be woven by 8 people in 5 days?

1. 153

2. 189

3. 127

4. 160

Q.

18.5 m of cloth costs ₹ 666. Find the cost of 3.8 m cloth

Answer should be ₹ 136.80

Q.

6 pipes can fill a tank in 4 hours. How many more pipes will be required to fill the same tank in 1 hour?

1. 24

2. 12

3. 18

4. 20

Q.

Weight of 8 identical article is 4.8 kg . what's the weight of 11 such identical?

Q.

Fill in the blanks:

In inverse proportion, if one quantity increases the other quantity ...........

Q. A hostel has a week's ration for 180 students. For how many days will the ration last, if 30 more students join the hostel?

1. 6 days
2. 3 days
3. 5 days
4. 4 days

Q. Calculate the volume occupied by 5.25 gram of nitrogen at 26degree Celsius and 74. 2cm of pressure.

Q.

If 8 pencils cost ₹24, a dozen of them will cost ___.

1. ₹30

2. ₹36

3. ₹40

4. ₹42

Q. Find:
$0.4÷2$

Q. When one amount decreases and another amount increases at the same rate is called as

1. Direct proportion
2. Inverse proportion
3. Constant

Q. 120 soldiers had groceries for 100 days. After 10 days, 20 soldiers were deputed to another post. For how many days will the remaining food last?

1. 108
2. 100
3. 110
4. 80

Q.

What are direct and inverse proportions?

Q. 9 men can finish a task in 4 days. How many days will 6 men take to finish the same task ?

1. 8
2. 6
3. 18
4. 9

Q. $\text{If}x\text{and}y\text{vary inversely, then find}$
$x_2\text{and}{y}_3.$

x	25	$x_2$	$\frac{55}{2}$
y	60	55	$y_3$

1. $x_2=\frac{30}{11}{y}_3=\frac{60}{11}$
2. $x_2=\frac{300}{11}{y}_3=\frac{610}{11}$
3. $x_2=\frac{250}{11}{y}_3=\frac{600}{11}$
4. $x_2=\frac{300}{11}{y}_3=\frac{600}{11}$

Q. Mohan lent ₹20000 to Rakesh for 5.5 years & ₹25000 to Dinesh for 4 years & receives a total sum of ₹19950 as interest. Find the rate per cent per annum, if it is same in both the cases .

Q.

Ram has to reach office in 2 hours. He can reach office in 2 hours if he travels at a speed of 75 kmph. But he reached office 1 hour late, find the speed at which he travelled?

1. 65 kmph

2. 45 kmph

3. 50 kmph

4. 55 kmph