EXERCISE 10 B
Q1 | Ex-10B | Class 8 | Direct and inverse variation | SChand Composite Maths | myhelper
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 : P∝1V or P=kV
⇒ PV = K
⇒ 500×2 = K
⇒K = 1000
(ii) The value of P when V = 5
Sol :
⇒P=kV
⇒P=10005
⇒P = 200
Q2 | Ex-10B | Class 8 | Direct and inverse variation | SChand Composite Maths | myhelper
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)
⇒No. of weeks∝1No. of mens or
⇒No. of weeks=kNo. of mens
⇒k = w×m , where k is variable constant
⇒k = 3×134 = 402
Now , m = 67 , d = ? ⇒ No. of weeks=kNo. of mens
⇒w=40267
⇒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
Q3 | Ex-10B | Class 8 | Direct and inverse variation | SChand Composite Maths | myhelper
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)
⇒S∝1T or
⇒S=kT
⇒k = S×T , where k is variable constant
⇒k = 65×12 = 780
Now , S = 78 , T = ? ⇒ S=kT
⇒S=78078
⇒S = 10
= 10 hours
Q4 | Ex-10B | Class 8 | Direct and inverse variation | SChand Composite Maths | myhelper
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)
⇒m=1T or
⇒m=kT
⇒k = T×m , where k is variable constant
⇒k = 16×210 = 3360
Now , T = 14 , m = ? ⇒ m=kT
⇒m=336014
⇒m = 240
To complete work in 14 months , we need
= 240 - 210
= 30 more men
Q5 | Ex-10B | Class 8 | Direct and inverse variation | SChand Composite Maths | myhelper
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) ,
⇒P∝1L or
⇒P=kL or
⇒k = P×L
⇒k = 540×28
⇒k = 15120 , where k is variable constant
Now , P = 360 , L = ? ⇒ , L=kP or
⇒L=15120360
⇒L = 42
= 42 lines per page
Q6 | Ex-10B | Class 8 | Direct and inverse variation | SChand Composite Maths | myhelper
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) ,
⇒M∝1C or
⇒M=kC or
⇒k = M×C
⇒k = 54×200
⇒k = 10800 , where k is variable constant
Now , C = 180 , M = ? ⇒ , M=kC or
⇒M=10800180
⇒M = 60
= 60 machines
Q7 | Ex-10B | Class 8 | Direct and inverse variation | SChand Composite Maths | myhelper
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) ,
⇒S∝1T or
⇒S=kT or
⇒k = S×T
⇒k = 135×4
⇒k = 540 , where k is variable constant
Now , S = 120 , T = ? ⇒ , T=kS or
⇒T=540120
⇒T = 4.5 seconds
= 4.5 seconds
Q8 | Ex-10B | Class 8 | Direct and inverse variation | SChand Composite Maths | myhelper
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) ,
⇒R∝1D or
⇒R=kD or
⇒k = R×D
⇒k = 200×35
⇒k = 7000 , where k is variable constant
Now , R = 250 , D = ? ⇒ , D=kR or
⇒D=7000250
⇒D = 28 days
Q9 | Ex-10B | Class 8 | Direct and inverse variation | SChand Composite Maths | myhelper
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)
⇒W∝1R or
⇒W=kR or
⇒k = W×R
⇒k = 2.8×765
⇒k = 2142 , where k is variable constant
Now , W = 1.7 , R = ? ⇒ , R=kW or
⇒R=21421.7
⇒R = 1260 times
= 1260 times
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