1.DIRECT PROPORTION: Two Quantities are said to be directly proportional, if on the increase (or decrease) of th one, the other increases(or decreases) to the same extent.
Ex:(i) Cost is directly proportional to the number of articles.(More articles,More cost).
(ii)Work done is directly proportional to the number of men working on it. (More men, more work).
2.INDIRECT PROPORTION: Two Quantities are said to be indirectly proportional,if on the increase of the one , the other decreases to the same extent and vice-versa.
Ex:(i) The time taken by a car covering a certain distance is inversely proportional to th speed of the car.(More speed, less is the time taken to cover the distance).
(ii)Time taken to finish a work is inversely proportional to the number of persons working at it. (More persons, less is the time taken to finish a job).
NOTE: In solving Questions by chain rule, we compare every item with the term to be found out.
1)If 15 toys cost Rs.234, what do 35 toys cost ?
Sol: Let the required cost be Rs. x then
more toys more cost(direct proportion)
15:35:: 234:x
(15*x)=(234*35)
x=(234*35) /(15)= 546 Rs
2)If 36 men can do a piece of work in 25hours, in how many hours will 15men do it?
Sol: Let the required number of hours be x.
less men more hours(Indirect proportion).
15:36::25:x
(15*x)=(36*25)
x=(36*25) /15
x=60
For 15 men it takes 60 hours.
3)If 9 engines consume 24metric tonnes of coal, when each is working 8 hours a day, how much coal will be required for 8 engines, each running 13 hours a day, it being given that 3 engines of former type consume as much as 4 engines of latter type?
Sol: Let 3 engines of former type consume 1 unit in 1 hour.
4 engines of latter type consume 1 unit in 1 hour.
1 engine of former type consumes 1/3 unit in 1 hour.
1 engine of latter type consumes ¼ unit in 1 hour.
Let required consumption of coal be x units.
Less engines, less coal consumed.(direct)
More working hours, more coal consumed(direct)
Less rate of consumption, less coal consumed (direct)
9:8
8:13 :: 24:x
1/3:1/4
(9*8*(1/3)*x)=(8*13*(1/4)*24)
24x=624
x=26 metric tonnes.
Ex:(i) Cost is directly proportional to the number of articles.(More articles,More cost).
(ii)Work done is directly proportional to the number of men working on it. (More men, more work).
2.INDIRECT PROPORTION: Two Quantities are said to be indirectly proportional,if on the increase of the one , the other decreases to the same extent and vice-versa.
Ex:(i) The time taken by a car covering a certain distance is inversely proportional to th speed of the car.(More speed, less is the time taken to cover the distance).
(ii)Time taken to finish a work is inversely proportional to the number of persons working at it. (More persons, less is the time taken to finish a job).
NOTE: In solving Questions by chain rule, we compare every item with the term to be found out.
Some Questions
1)If 15 toys cost Rs.234, what do 35 toys cost ?
Sol: Let the required cost be Rs. x then
more toys more cost(direct proportion)
15:35:: 234:x
(15*x)=(234*35)
x=(234*35) /(15)= 546 Rs
2)If 36 men can do a piece of work in 25hours, in how many hours will 15men do it?
Sol: Let the required number of hours be x.
less men more hours(Indirect proportion).
15:36::25:x
(15*x)=(36*25)
x=(36*25) /15
x=60
For 15 men it takes 60 hours.
3)If 9 engines consume 24metric tonnes of coal, when each is working 8 hours a day, how much coal will be required for 8 engines, each running 13 hours a day, it being given that 3 engines of former type consume as much as 4 engines of latter type?
Sol: Let 3 engines of former type consume 1 unit in 1 hour.
4 engines of latter type consume 1 unit in 1 hour.
1 engine of former type consumes 1/3 unit in 1 hour.
1 engine of latter type consumes ¼ unit in 1 hour.
Let required consumption of coal be x units.
Less engines, less coal consumed.(direct)
More working hours, more coal consumed(direct)
Less rate of consumption, less coal consumed (direct)
9:8
8:13 :: 24:x
1/3:1/4
(9*8*(1/3)*x)=(8*13*(1/4)*24)
24x=624
x=26 metric tonnes.
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