## EXERCISE 10 B

Question 1

**The pressure P of an enclosed gas , held at a constant temperature , is inversely proportional to the volume V of the gas . Express P in terms of V and the constant of variations K . Calculate**

**(i) The value of K when P = 500 and V = 2**

Sol :

Given : or

⇒ PV = K

⇒ 500×2 = K

⇒K = 1000

**(ii) The value of P when V = 5**

Sol :

⇒

⇒

⇒P = 200

Question 2

**How many days would it take 67 men to build a wall which 134 mens can build in 3 weeks ?**

Sol :

Number of men (m) | 134 | 67 |
---|---|---|

Number of weeks(w) | 3 |

As number of weeks (w) varies inversely with number of mens (m)

⇒ or

⇒

⇒k = w×m , where k is variable constant

⇒k = 3×134 = 402

Now , m = 67 , d = ? ⇒

⇒

⇒w = 6

= 6 weeks

**ALTERNATE METHOD**

134÷67=2

Simple explanation through logic:

If 2x the amount of people takes a certain time to complete a task, half the amount of people will take 2x the time to complete the task.

3 weeks × 2 = 6 weeks

6 weeks = 42 days

**Some basic concept**

Why we are not dividing 134 by 3 ?

Answer : Because No. of mens is inversely proportional to no . of weeks in other words on increasing first value(no. of mens) then other value decreases(no. of weeks)

Or

Why we are multiplying 134 by 3 ?

Answer : To understand this firstly lets discuss why we use multiplication

Suppose we have to give 2 pencil to every five person , then whats the Total no. of pencils

2 + 2 + 2 + 2 + 2 = 10 or 2×5 = 10

In the same way 134 mens work every week , total 3 weeks to complete work

No . of mens in 1st week + No. of mens work in 2nd week + No. of mens work in 3rd week = 402 or No. of mens ×3 = 402

402/67= 6 weeks

Question 3

**A car can complete a certain journey in 12 hours if it travels at 65 km/h . How much time will it take if it travels at 78 km/h ?**

Sol :

Speed(S) | 65 km/p | 78 km/h |
---|---|---|

Time (T) | 12 hours |

As Speed (S) varies inversely with Time (T)

⇒ or

⇒

⇒k = S×T , where k is variable constant

⇒k = 65×12 = 780

Now , S = 78 , T = ? ⇒

⇒

⇒S = 10

= 10 hours

Question 4

**A workforce of 210 men with a contractor can finish a work in 16 months . How many more man men should be employed so that the work is completed in 14 months ?**

Sol :

Number of men (m) | 210 | |
---|---|---|

Time(T) | 16 months | 14 months |

As Number of mens (m) varies inversely with Time (T)

⇒ or

⇒

⇒k = T×m , where k is variable constant

⇒k = 16×210 = 3360

Now , T = 14 , m = ? ⇒

⇒

⇒m = 240

To complete work in 14 months , we need

= 240 – 210

= 30 more men

Question 5

**It is found that a book will contains 540 pages if 28 lines are allowed in a page . How many lines should be allowed in a page if the book has to contain 360 pages ?**

Sol :

Number of pages (P) | 540 | 360 |
---|---|---|

Lines (L) | 28 |

As Number of pages (P) varies inversely with Lines (L) ,

⇒ or

⇒ or

⇒k = P×L

⇒k = 540×28

⇒k = 15120 , where k is variable constant

Now , P = 360 , L = ? ⇒ , or

⇒

⇒L = 42

= 42 lines per page

Question 6

**Sreyash has enough money to buy 54 machines worth 200 each . How many machines can he buys if he gets a discount of 20 on each machine ?**

Sol :

Number of Machines (M) | 54 | |
---|---|---|

Cost of each (C) | 200 | 200 – 20 = 180 |

As Number of Machines (M) varies inversely with Cost (C) ,

⇒ or

⇒ or

⇒k = M×C

⇒k = 54×200

⇒k = 10800 , where k is variable constant

Now , C = 180 , M = ? ⇒ , or

⇒

⇒M = 60

= 60 machines

Question 7

**If a ball moves at 135 m/s , it will strike an object in 4 seconds . If it moves at 120 m/s , how long will it takes to strike the same objects ?**

Sol :

Speed (S) | 135 m/s | 120 m/s |
---|---|---|

Time (T) | 4 seconds |

As Speed (S) varies inversely with Time (T) ,

⇒ or

⇒ or

⇒k = S×T

⇒k = 135×4

⇒k = 540 , where k is variable constant

Now , S = 120 , T = ? ⇒ , or

⇒

⇒T = 4.5 seconds

= 4.5 seconds

Question 8

**A man eats 200 g of rice a day and he has enough rice to last him 35 days . How long would the stock of rice last him if he were to eat 250 g of rice a day ?**

Sol :

Rice (R) | 200 g | 250 g |
---|---|---|

Number of Days (D) | 35 days |

As Rice (R) varies inversely with Number of Days (D) ,

⇒ or

⇒ or

⇒k = R×D

⇒k = 200×35

⇒k = 7000 , where k is variable constant

Now , R = 250 , D = ? ⇒ , or

⇒

⇒D = 28 days

Question 9

**A wheel of circumference 2.8 m revolve 765 times in traversing a certain distance . How many revolutions does a wheel of circumference 1.7 m make in traversing the same distance .**

Sol :

Circumference of wheel (W) | 2.8 m | 1.7 m |
---|---|---|

Number of Revolution (R) | 765 |

As Circumference of wheel (W) varies inversely with Number of Revolution (R)

⇒ or

⇒ or

⇒k = W×R

⇒k = 2.8×765

⇒k = 2142 , where k is variable constant

Now , W = 1.7 , R = ? ⇒ , or

⇒

⇒R = 1260 times

= 1260 times