Exercise 10 B
Question 1
1. State the relationship between the given variables as an equation, using $k$ for the constant of variation.
(i) The volume $V$ of a gas at a fixed temperature varies inversely as the pressure $P$.
(ii) The current $I$ in an electrical circuit of fixed voltage, varies inversely as the resistance $R$.
(iii) The height $h$ of a cylinder of fixed volume, varies inversely as the area $A$ of the base.
(iv) The frequency $f$ of an electromagnetic wave is inversely proportional to the length $l$ of the wave.
2. Fill in the blanks in the following tables by determining first whether x and y vary directly or inversely :
(a)
| x | 3 | 6 | ? | 27 | ? |
| y | 11 | 22 | 33 | ? | 880 |
(b)
| x | 30 | 20 | 15 | ? | ? |
| y | 6 | 4 | ? | 2 | 1 |
(c)
| x | 2 | 3 | 4 | ? | 8 |
| y | 48 | ? | 24 | 16 | ? |
(d)
| x | 1 | 5 | 10 | ? | ? |
| y | 125 | ? | 12.5 | 5 | 1 |
3. (i) If $y$ varies inversely as $x$, and if $y=9$ when $x=2$, find $y$ when $x=3$.
(ii) If $u$ is inversely proportional to $v$, and if $u=12$ when $v=3$, find $u$ when $v=9$.
(iii) If $c$ is inversely proportional to $d$, and if $c=18$ when $d=\frac{2}{3}$, find $d$ when $c=\frac{6}{7}$.
(iv) If $m$ is inversely proportional to $n$, and if $m=0.02$ when $n=5$, find $m$ when $n=0.2$.
4. Navin cycles to his school at an average speed of $12 \mathrm{~km} / \mathrm{hr}$. It takes him 20 minutes to reach the school. If he wants to reach his school in 15 minutes, what should be his average speed ?
5. The time needed to travel from one place to another is inversely proportional to the speed. A person travelling $72 \mathrm{~km} / \mathrm{hr}$ can go from Dehradun to Lucknow in 10 hours. How fast must the person travel to make the trip in 9 hours?
6. 28 pumps can empty a reservoir in 18 hours. In how many hours can 42 such pumps do the same work?
7. A stock of food grains is enough for 400 persons for 9 days. How long will the same stock last for 300 persons?
8. A contractor who had a work force of 630 persons, undertook to complete a portion of a stadium in 14 months. He was asked to complete the job in 9 months. How many extra persons had he to employ?
9. Working 4 hours a day, Savita can type a manuscript in 15 days. How many hours a day should she work so as to finish the work in 10 days ?
10. A train moving at a speed of $60 \mathrm{~km} / \mathrm{hr}$ covers a certain distance in $7.5$ hours. What should be the speed of the train to cover the same distance in 6 hours?
11. A garrison of 800 men had provisions for 39 days. However, a reinforcement of 500 men arrived. For how many days will the food last now ?
12. A besieged town has provisions to last for 3 weeks. Its population is 22400 . How many people must be sent away in order that the provisions may last for 7 weeks?
13. A hostel had rations for 60 days for 500 students. After 12 days, 300 more students join the hostel. How long will the remaining rations last?
Multiple Choice Questions (MCQS)
14. $x$ and $y$ vary inversely as each other. When $x=10, y=6$. Which of the following is not a possible pair of corresponding values of $x$ and $y$.
(a) 15 and 4
(b) 20 and 3
(c) $1.5$ and 30
(d) $0.6$ and 100
15. If $a$ varies inversely as $b+2$ and if $a=8$ when $b=1.5$, find $a$ when $b=5$.
(a) $2 \frac{2}{5}$
(b) $5 \frac{3}{5}$
(c) 4
(d) $4 \frac{2}{5}$
16. The number of hours needed to clear the trees from some land is inversely proportional to the number of people who are working. If it would take 4 people 15 hours to do the job, how many people would be needed to complete the job in 6 hours?
(a) 22 people
(b) 8 people
(c) 10 people
(d) 15 people
17. A pulley revolves at a speed that is inversely proportional to its diameter. A pulley with a diameter of $12 \mathrm{~cm}$ is belted to a pulley with a diameter of $8 \mathrm{~cm}$. If the smaller pulley is revolving at a rate of $96 \mathrm{rpm}$ (revolutions per minute), how fast is the larger pulley revolving?
(a) $144 \mathrm{rpm}$
(b) $64 \mathrm{rpm}$
(c) $40 \mathrm{rpm}$
(d) $48 \mathrm{rpm}$
High Order Thinking Skills (HOTS)
18. A group of 210 men had provisions for 60 days. After 10 days, 60 men left. How long will the remainign food last ?
[Hint. The remaining food would have lasted 50 days for 210 men. Find out how long will the food last for 150 men].
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