Different kinds of quantities are connected to one another so that we know how much of one quantity is equivalent to a given quantity of a second etc. We can determine how many of the last kind is equivalent to a given quantity of first kind by the chain rule .
- DIRECT PROPORTION : Two quantities are said to be directly proportional, id on the increase (or decrease ) of the one, the other increases to the same extent.
- 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.
Results
#1. 4 mat- weavers can weave 4 mats in 4 days. At the same rate, how many mats would be woven by 8 mat- weavers in 8 days?
4 mat- weavers can weave 4 mats in 4 days. At the same rate, how many mats would be woven by 8 mat- weavers in 8 days?
Let the required number of bottles be x.
More weavers, More mats ( Direct proportion)
More days, More mats ( Direct proportion)
weavers 4 : 8
Days 4 : 8 ::4 : x
4 * 4* x= 8 * 8* 4
x= (8*8*4)/(4*4)
= 16
#2. If a quarter Kg of potato costs 60 paise, how many paise will 200 gm cost ?
If a quarter Kg of potato costs 60 paise, how many paise will 200 gm cost ?
Let the required cost be x paise.
Less Weight,Less cost ( Direct proportion)
250 : 200::60 : x
250 *x=(200*60)
x=(200*60)/250
x=48
#3. In a camp, 95 men had provisions for 200 days. After 5 days, 30men left the camp. For how many days will the remaining food last now ?
Let the remaining food will last for x days
95 men had provisions for 195 days.
65 men had provisions for x days
less men. More days
65 : 95 :: 195 : x
(65*x)=(95*195)
x= 95*195/65
=285
#4. Some persons can do a piece of work in 12 days. Two times the number of such persons will do half of that work in :
Some persons can do a piece of work in 12 days. Two times the number of such persons will do half of that work in :
Men = 2x : x
Work = 1: 1/2 :: 12 : z
(2x * 1 * z ) =
(x * 1/2 * 12 )
2xz = 6x
z = 3
#5. A rope makes 70 rounds of the circumference of cylinder whose radius of the base is 14 cm . How many time can it go round a cylinder with radius 20 cm ?
A rope makes 70 rounds of the circumference of cylinder whose radius of the base is 14 cm . How many time can it go round a cylinder with radius 20 cm ?
Let the required number of round be x
More radius , less round
20 : 14 :: 70 ; x
= (20 * x )
= ( 14 * 70 )
x = 14*70/20
x = 49
Hence the required number of round = 49
#6. If 18 binder bind 900 books in 10 days , how many binder will be required to bind the 660 books in 12 days ?
If 18 binder bind 900 books in 10 days , how many binder will be required to bind the 660 books in 12 days ?
Let the required number of binder be x
Less books ,Less binder ( Direct proportion )
More days , Less binder ( Indirect proportion )
Books 900 : 600
Days 12 : 10 :: 18 : x
= ( 900 * 12 * x )
= ( 600 * 10 * 18 )
x = 600*10*18/900*12
= 11
#7. If carpenters , working 6 hours a days can makes 460 chair in 24 days how any chair in 18 carpenter make in 36 days each working 8 hours a days ?
If carpenters , working 6 hours a days can makes 460 chair in 24 days how any chair in 18 carpenter make in 36 days each working 8 hours a days ?
Let the required number of chair be x
More carpenter , More chair
More hours per days , More chair
More days , More chair
carpenter 12 : 18
hours in per day 6 : 8
Days 24 : 36 ::460 : x
= ( 12*6*24*x )
= ( 18*8*36*460 )
x = ( 18*8*36*460) /( 12*6*24 )
= 1380
#8. If 7 spiders makes 7 webs in 7 days ,then 1 spider will make 1 web in how many day ?
If 7 spiders makes 7 webs in 7 days ,then 1 spider will make 1 web in how many day ?
Let the required number of days be x
Less spider ,More days
Less webs ,Less days
Spider 1 : 7
webs 7 : 1 ::7 : x
= 1*7*x
= 7*1*7
x = 7
#9. If 8 men can reap 80 hectares in 24 days , then how many hectares can 36 men reap in 30 days ?
If 8 men can reap 80 hectares in 24 days , then how many hectares can 36 men reap in 30 days ?
Let the required number of hectares be x ,Then
More men ,More hectors
More days,More hectors
Men 8 : 36
Days 24 :30 ::80 : x
8*24*x =36*30*80
x= ( 36*30*80 )/(8*24)
x = 450
#10. If 3/5 of a cistern is filled in 1 minute How much more time will be required to fill the rest of it ?
If 3/5 of a cistern is filled in 1 minute How much more time will be required to fill the rest of it ?
Let the required time x sec
Parts filled = 3/5 remaining part = (1 – 3/5 ) = 2/5
Less part ,Less time
3/5 : 2/5 :: 60 : x
( 3/5*x) = (2/5 *60)
x = 40
#11. 39 persons repair a road in 12 days , working 5 hours a days . In how many days will 30 persons , working 6 hours a days , complete the work ?
39 persons repair a road in 12 days , working 5 hours a days . In how many days will 30 persons , working 6 hours a days , complete the work ?
Let the required number of days be x
Less person ,More days
More working hrs per days ,Less days
persons 30 : 39
working are per day 6 : 5 :: 12 : x
30*6*x = 39*5*12
x =( 39*5*12)/(30*60)
x = 13
#12. 10 men working 6 hours a day can complete a work in 18 days . How many hours a day must 15 men work to complete the same work in 12 days ?
10 men working 6 hours a day can complete a work in 18 days . How many hours a day must 15 men work to complete the same work in 12 days ?
Let the required number of hours per days be x More men , Less hours per days
Less days , more hours per days
Men 15 : 10
Days 12 ; 18 :: 6 : x
15*12*x=10*18*6
x = 10*18*6/15*12
x = 6
#13. In a dairy farm , 40 cows eat 40 bags of husk in 40 days , In how many days 1 cow will eat 1 bag of husk ?
In a dairy farm , 40 cows eat 40 bags of husk in 40 days , In how many days 1 cow will eat 1 bag of husk ?
Let the required number of days be x
Less cow , More day
Les bags ,Less days
cows 1 : 40
Bags 40 : 1 :: 40 : x
1*40*x =40*1*40
x = 40
#14. If the cost of x metres of wire is d rupees , then what is cost of y metres of wire at same rate ?
If the cost of x metres of wire is d rupees , then what is cost of y metres of wire at same rate ?
Cost of x metres = rupees d
Cost of 1 metres = rupees (d/x)
cost of y metres = rupees (d/x*y)
= Rs. (yd/x)
#15. If the price of 6 toys is rupees 264.37 , What will approximate price of 5 toys ?
If the price of 6 toys is rupees 264.37 , What will approximate price of 5 toys ?
Let the required price be rs.x
Less toys, Less cost
6 : 5 :: 264 : x
6x (5*264)
x = (5*264)/6
x = 220
#16. An industrial loom weaves 0.128 meters of clothes every second . Approximately How many seconds will it take for the loom to weaves 25 meters of cloths ?
An industrial loom weaves 0.128 meters of clothes every second . Approximately How many seconds will it take for the loom to weaves 25 meters of cloths ?
Let the required time be x seconds then , More metres more time
0.128*x = 25*1
x = 25/0.128 = 25*1000/128
x = 195.31
#17. If 12 men do a piece of work in 80 days in how many days will 16 men do it ?
If 12 men do a piece of work in 80 days in how many days will 16 men do it ?
correct answer is 60
#18. If 120 men can do a job in 100 days in how many days will 150 men do it ?
If 120 men can do a job in 100 days in how many days will 150 men do it ?
correct answer is 80 days
#19. If the rent for grazing 40 goats for 20 days is Rs. 370 how many goats can graze for Rs. 111 ?
If the rent for grazing 40 goats for 20 days is Rs. 370 how many goats can graze for Rs. 111 ?
correct answer is 8
#20. If Rs. 80 maintain a family of 4 person for 40 days for how long will Rs. 105 maintain a family of 6 person ?
If Rs. 80 maintain a family of 4 person for 40 days for how long will Rs. 105 maintain a family of 6 person ?
correct answer is 35 days