Chain Rule Examples,Chain Rule Formula
In our blog today i am going to tell you Chain Rule Problems,chain rule examples and chain rule formula. you can check chain rule tricks,chain rule short tricks here. Check your Strength in Chain Rule Aptitude Question Problem. there are total 30 question and total time will be 30 minutes. jobriya.co.in provide you chain rule short tricks with the help of this tricks you can solve chain rule problem within second.
Introduction:
1. Direct Proportion: Two quantities are said to be directly proportional, if on the increase (or decrease) of the one, the other increases (or decreases) to the same
Ex. 1. Cost is directly proportional to the number of articles.(More Articles, More Cost)
Ex. 2. 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 viceversa.
Ex. 1. The time taken by a car in covering a certain distance is inversely proportional to the speed of the car. (More speed, Less is the time taken to cover a distance)
Ex. 2. Time taken to finish a work is inversely proportional to the num of persons working at it. (More persons, Less is the time taken to finish a job)
Remark: In solving questions by chain rule, we compare every item with the term to be found out.
Chain Rule Examples
Ex. 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 x) = (35 x 234) = x=(35 X 234)/15 =546
Hence, the cost of 35 toys is Rs. 546.
Ex. 2. If 36 men can do a piece of work in 25 hours, in how many hours will 15 men do it ?
Sol. Let the required number of hours be x. Then, Less men, More hours (Indirect Proportion)
15 : 36 : : 25 : x =(15 x x) = (36 x 25) =(36 x 25)/15 = 60
Hence, 15 men can do it in 60 hours.
Ex. 3. If the wages of 6 men for 15 days be Rs.2100, then find the wages of for 12 days.
Sol. Let the required wages be Rs. x.
More men, More wages (Direct Proportion)
Less days, Less wages (Direct Proportion)
Men 6: 9 : :2100:x
Days 15:12
Therefore (6 x 15 x x)=(9 x 12 x 2100) = x=(9 x 12 x 2100)/(6 x 15)=2520
Hence the required wages are Rs. 2520.
Ex. 4. If 20 men can build a wall 66 metres long in 6 days, what length of a similar can be built by 86 men in 8 days?
Sol. Let the required length be x metres
More men, More length built (Direct Proportion)
Less days, Less length built (Direct Proportion)
Men 20: 35
Days 6: 3 : : 56 : x
Therefore (20 x 6 x x)=(35 x 3 x 56)x=(35 x 3 x 56)/120=49
Hence, the required length is 49 m.
Ex. 5. If 15 men, working 9 hours a day, can reap a field in 16 days, in how many days will 18 men reap the field, working 8 hours a day?
Sol. Let the required number of days be x.
More men, Less days (indirect proportion)
Less hours per day, More days (indirect proportion)
Men 18 : 15
Hours per day 8: 9 } : :16 : x
(18 x 8 x x)=(15 x 9 x 16) x=(44 x 15)144 = 15
Hence, required number of days = 15.
Ex. 6. If 9 engines consume 24 metric tonnes of coal, when each is working 8 hours day, bow much coal will be required for 8 engines, each running 13hours 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.
Then, 4 engines of latter type consume 1 unit in 1 hour.
Therefore 1 engine of former type consumes(1/3) unit in 1 hour.
1 engine of latter type consumes(1/4) unit in 1 hour.
Let the required consumption of coal be x units.
Less engines, Less coal consumed (direct proportion)
More working hours, More coal consumed (direct proportion)
Less rate of consumption, Less coal consumed(direct prportion)
Number of engines 9: 8
Working hours 8 : 13 } :: 24 : x
Rate of consumption (1/3):(1/4)
[ 9 x 8 x (1/3) x x) = (8 x 13 x (1/4) x 24 ) = 24x = 624 = x = 26.
Hence, the required consumption of coal = 26 metric tonnes.
Ex. 7. A contract is to be completsd in 46 days sad 117 men were said to work 8 hours a day. After 33 days, (4/7) of the work is completed. How many additional men may be employed so that the work may be completed in time, each man now working 9 hours a day?
Sol. Remaining work = (1(4/7) =(3/7)
Remaining period = (46 – 33) days = 13days
Let the total men working at it be x.
Less work, Less men (Direct Proportion)
Less days, More men (Indirect Proportion)
More Hours per Day, Less men (Indirect Proportion)
Work (4/7): (3/7)
Days 13:33 } : : 117: x
Hrs/day 9 : 8
Therefore (4/7) x 13 x 9 x x =(3/7) x 33 x 8 x 117 or x=(3 x 33 x 8 x 117)/(4 x 13 x 9)=198 Additional men to be employed = (198 – 117) = 81.
Ex. 8. A garrison of 3300 men had provisions for 32 days, when given at the rate of 860 gns per head. At the end of 7 days, a reinforcement arrives and it was for that the provisions wi1l last 17 days more, when given at the rate of 826 gms per head, What is the strength of the reinforcement?
Sol. The problem becomes:
3300 men taking 850 gms per head have provisions for (32 – 7) or 25 days,
How many men taking 825 gms each have provisions for 17 days?
Less ration per head, more men (Indirect Proportion)
Less days, More men (Indirect Proportion)
Ration 825 : 850
Days 17: 25 } : : 3300 : x
(825 x 17 x x) = 850 x 25 x 3300 or x = (850 x 25 x 3300)/(825 x 17)=5000
Strength of reinforcement = (5500 – 3300) = 1700.
Chain Rule Quiz
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Question 1 of 25
1. Question
1 pointsIf 16 toys cost 240, then what do 40 toys cost ?
Correct
Although we can first calculate the cost of one toy and then can multiply it with 40 to get the result.
but we will solve it with chain rule so that we can prepare ourself for other complex problems which we can solve easily by applying this rule.Let the required cost be Rs. x
More toys means More Cost. (Direct Proportion)15:40::240:x=>x=240∗4015=>x=64015:40::240:x=>x=240∗4015=>x=640
So 40 toys will cost Rs 640
Incorrect
Although we can first calculate the cost of one toy and then can multiply it with 40 to get the result.
but we will solve it with chain rule so that we can prepare ourself for other complex problems which we can solve easily by applying this rule.Let the required cost be Rs. x
More toys means More Cost. (Direct Proportion)15:40::240:x=>x=240∗4015=>x=64015:40::240:x=>x=240∗4015=>x=640
So 40 toys will cost Rs 640

Question 2 of 25
2. Question
1 pointsIf the cost of x metres of wire is d rupees, then what is the cost of y metres of wire at the same rate ?
Correct
Option C
Incorrect
Option C

Question 3 of 25
3. Question
1 pointsIf the price of 23 toys is 276, then what will the price of 12 toys ?
Correct
Less toys, Less Price (Direct Proportion)
So, let the price be Rs. x
then,23:12::276:x=>x=276∗1223=>x=14423:12::276:x=>x=276∗1223=>x=144
So price of 12 toys will be Rs. 144
Incorrect
Less toys, Less Price (Direct Proportion)
So, let the price be Rs. x
then,23:12::276:x=>x=276∗1223=>x=14423:12::276:x=>x=276∗1223=>x=144
So price of 12 toys will be Rs. 144

Question 4 of 25
4. Question
1 pointsIf a quarter kg of potato costs 60 paise, how many paise will 200gm cost ?
Correct
Quarter of Kg means 250 gm
Less weight, less price (Direct Proportion)
So,250:200::60:x=>x=200∗60250=>x=48250:200::60:x=>x=200∗60250=>x=48
So 200 gm will cost 48 paise.
Incorrect
Quarter of Kg means 250 gm
Less weight, less price (Direct Proportion)
So,250:200::60:x=>x=200∗60250=>x=48250:200::60:x=>x=200∗60250=>x=48
So 200 gm will cost 48 paise.

Question 5 of 25
5. Question
1 pointsAn industrial loom weaves 0.128 metres of cloth every second. Approximately, how many seconds will it take for the loom to weave 25 metre of cloth ?
Correct
Let the time required by x seconds.
Then, More cloth means More time (Direct Proportion)
So,0.128:1::25:x=>x=25∗10.128=>x=195.310.128:1::25:x=>x=25∗10.128=>x=195.31
So time will be approx 195 seconds
Incorrect
Let the time required by x seconds.
Then, More cloth means More time (Direct Proportion)
So,0.128:1::25:x=>x=25∗10.128=>x=195.310.128:1::25:x=>x=25∗10.128=>x=195.31
So time will be approx 195 seconds

Question 6 of 25
6. Question
1 pointsA flagstaff 17.5 metre high casts a shadow of length 40.25 metre. The height of building, which casts a shadow of length 28.75 metre under similar conditions will be :
Correct
Less shadow, Less Height (Direct Proportion)
So, let height of building be x metre
then,
40.25:17.5::28.75:x=>x=17.5∗28.7540.25=>x=12.540.25:17.5::28.75:x=>x=17.5∗28.7540.25=>x=12.5So height of building should be 12.5 metre
Incorrect
Less shadow, Less Height (Direct Proportion)
So, let height of building be x metre
then,
40.25:17.5::28.75:x=>x=17.5∗28.7540.25=>x=12.540.25:17.5::28.75:x=>x=17.5∗28.7540.25=>x=12.5So height of building should be 12.5 metre

Question 7 of 25
7. Question
1 points36 men can complete a piece of work in 18 days. In how many days will 27 men complete the same work ?
Correct
Less Men, means more Days {Indirect Proportion}
Let the number of days be x
then,27 : 36 :: 18 : x
[Please pay attention, we have written 27 : 36 rather than 36 : 27, in indirect proportion, if you get it then chain rule is clear to you :)]x=36∗1827x=24x=36∗1827x=24
So 24 days will be required to get work done by 27 men.Incorrect
Less Men, means more Days {Indirect Proportion}
Let the number of days be x
then,27 : 36 :: 18 : x
[Please pay attention, we have written 27 : 36 rather than 36 : 27, in indirect proportion, if you get it then chain rule is clear to you :)]x=36∗1827x=24x=36∗1827x=24
So 24 days will be required to get work done by 27 men. 
Question 8 of 25
8. Question
1 pointsIn a camp, there is a meal for 120 men or 200 children. If 150 children have taken the meal, how many men will be catered to with the remaining meal ?
Correct
There is meal for 200 children. 150 children have taken the meal.
Remaining meal is to be catered to 50 children.
Now, 200 children = 120 menSo, 50 Children = 120/200 * 50 = 30 men
Incorrect
There is meal for 200 children. 150 children have taken the meal.
Remaining meal is to be catered to 50 children.
Now, 200 children = 120 menSo, 50 Children = 120/200 * 50 = 30 men

Question 9 of 25
9. Question
1 points4 matweavers can weave 4 mats in 4 days. At the same rate, how many mats would be woven by 8 mat weavers in 8 days ?
Correct
Please always remember, that what exactly we need to calculate before applying chain formula. As in this question we need to find how many mats, RIGHT !
So we will compare everything with “number of mats”
As,More men, More number of mats (Direct Proportion)
More days, More number of mats (Direct Proportion)So, it can be solved as,
[WeaversDays4488]::4:x=>x∗4∗4=8∗8∗4=>x=16[Weavers48Days48]::4:x=>x∗4∗4=8∗8∗4=>x=16
Incorrect
Please always remember, that what exactly we need to calculate before applying chain formula. As in this question we need to find how many mats, RIGHT !
So we will compare everything with “number of mats”
As,More men, More number of mats (Direct Proportion)
More days, More number of mats (Direct Proportion)So, it can be solved as,
[WeaversDays4488]::4:x=>x∗4∗4=8∗8∗4=>x=16[Weavers48Days48]::4:x=>x∗4∗4=8∗8∗4=>x=16

Question 10 of 25
10. Question
1 pointsIn a dairy farm, 40 cows eat 40 bags of husk in 40 days. In how many days one cow will eat one bag of husk ?
Correct
Less Cows, More days (Indirect Proportion)
Less bags, Less days (Direct Proportion)[CowsBags140401]::40:x=>x∗40∗1=40∗1∗40=>x=40[Cows140Bags401]::40:x=>x∗40∗1=40∗1∗40=>x=40
Incorrect
Less Cows, More days (Indirect Proportion)
Less bags, Less days (Direct Proportion)[CowsBags140401]::40:x=>x∗40∗1=40∗1∗40=>x=40[Cows140Bags401]::40:x=>x∗40∗1=40∗1∗40=>x=40

Question 11 of 25
11. Question
1 points10 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 work in 12 days ?
Correct
More Men, Less Hours {Indirect Proportion}
Less Days, More Hours {Indirect Proportion}
[MenDays15121018]::6:x=>x∗15∗12=10∗18∗6=>x=10∗18∗615∗12=>x=6[Men1510Days1218]::6:x=>x∗15∗12=10∗18∗6=>x=10∗18∗615∗12=>x=6Incorrect
More Men, Less Hours {Indirect Proportion}
Less Days, More Hours {Indirect Proportion}
[MenDays15121018]::6:x=>x∗15∗12=10∗18∗6=>x=10∗18∗615∗12=>x=6[Men1510Days1218]::6:x=>x∗15∗12=10∗18∗6=>x=10∗18∗615∗12=>x=6 
Question 12 of 25
12. Question
1 points3 pumps, working 8 hours a day, can empty a tank in 2 days. How many hours a day must 4 pumps work to empty the tank in 1 day?
Correct
Let the required number of working hours per day be x.
More pumps, Less working hours per day (Indirect Proportion)
Less days, More working hours per day (Indirect Proportion)
Pumps 4 : 3 :: 8 : x Days 1 : 2 4 x 1 x x = 3 x 2 x 8
x = (3 x 2 x 8) (4) x = 12.
Incorrect
Let the required number of working hours per day be x.
More pumps, Less working hours per day (Indirect Proportion)
Less days, More working hours per day (Indirect Proportion)
Pumps 4 : 3 :: 8 : x Days 1 : 2 4 x 1 x x = 3 x 2 x 8
x = (3 x 2 x 8) (4) x = 12.

Question 13 of 25
13. Question
1 pointsIf the cost of x metres of wire is d rupees, then what is the cost of y metres of wire at the same rate?
Correct
Cost of x metres = Rs. d.
Cost of 1 metre = Rs. d x Cost of y metres = Rs. d . y = Rs. yd . x x Incorrect
Cost of x metres = Rs. d.
Cost of 1 metre = Rs. d x Cost of y metres = Rs. d . y = Rs. yd . x x 
Question 14 of 25
14. Question
1 pointsRunning at the same constant rate, 6 identical machines can produce a total of 270 bottles per minute. At this rate, how many bottles could 10 such machines produce in 4 minutes? Correct
Let the required number of bottles be x.
More machines, More bottles (Direct Proportion)
More minutes, More bottles (Direct Proportion)
Machines 6 : 10 :: 270 : x Time (in minutes) 1 : 4 6 x 1 x x = 10 x 4 x 270
x = (10 x 4 x 270) (6) x = 1800.
Incorrect
Let the required number of bottles be x.
More machines, More bottles (Direct Proportion)
More minutes, More bottles (Direct Proportion)
Machines 6 : 10 :: 270 : x Time (in minutes) 1 : 4 6 x 1 x x = 10 x 4 x 270
x = (10 x 4 x 270) (6) x = 1800.

Question 15 of 25
15. Question
1 points39 persons can repair a road in 12 days, working 5 hours a day. In how many days will 30 persons, working 6 hours a day, complete the work? Correct
Let the required number of days be x.
Less persons, More days (Indirect Proportion)
More working hours per day, Less days (Indirect Proportion)
Persons 30 : 39 :: 12 : x Working hours/day 6 : 5 30 x 6 x x = 39 x 5 x 12
x = (39 x 5 x 12) (30 x 6) x = 13.
Incorrect
Let the required number of days be x.
Less persons, More days (Indirect Proportion)
More working hours per day, Less days (Indirect Proportion)
Persons 30 : 39 :: 12 : x Working hours/day 6 : 5 30 x 6 x x = 39 x 5 x 12
x = (39 x 5 x 12) (30 x 6) x = 13.

Question 16 of 25
16. Question
1 pointsA man completes of a job in 10 days. At this rate, how many more days will it takes him to finish the job?
Correct
Work done = 5 8 Balance work = 1 – 5 = 3 8 8 Let the required number of days be x.
Then, 5 : 3 = :: 10 : x 5 x x = 3 x 10 8 8 8 8 x = 3 x 10 x 8 8 5 x = 6.
Incorrect
Work done = 5 8 Balance work = 1 – 5 = 3 8 8 Let the required number of days be x.
Then, 5 : 3 = :: 10 : x 5 x x = 3 x 10 8 8 8 8 x = 3 x 10 x 8 8 5 x = 6.

Question 17 of 25
17. Question
1 pointsIf a quarter kg of potato costs 60 paise, how many paise will 200 gm cost?
Correct
Let the required weight be x kg.
Less weight, Less cost (Direct Proportion)
250 : 200 :: 60 : x 250 x x = (200 x 60)
x= (200 x 60) 250 x = 48.
Incorrect
Let the required weight be x kg.
Less weight, Less cost (Direct Proportion)
250 : 200 :: 60 : x 250 x x = (200 x 60)
x= (200 x 60) 250 x = 48.

Question 18 of 25
18. Question
1 pointsIn a dairy farm, 40 cows eat 40 bags of husk in 40 days. In how many days one cow will eat one bag of husk? Correct
Let the required number of days be x.
Less cows, More days (Indirect Proportion)
Less bags, Less days (Direct Proportion)
Cows 1 : 40 :: 40 : x Bags 40 : 1 1 x 40 x x = 40 x 1 x 40
x = 40.
Incorrect
Let the required number of days be x.
Less cows, More days (Indirect Proportion)
Less bags, Less days (Direct Proportion)
Cows 1 : 40 :: 40 : x Bags 40 : 1 1 x 40 x x = 40 x 1 x 40
x = 40.

Question 19 of 25
19. Question
1 pointsA wheel that has 6 cogs is meshed with a larger wheel of 14 cogs. When the smaller wheel has made 21 revolutions, then the number of revolutions mad by the larger wheel is:
Correct
Let the required number of revolutions made by larger wheel be x.
Then, More cogs, Less revolutions (Indirect Proportion)
14 : 6 :: 21 : x 14 x x = 6 x 21
x = 6 x 21 14 x = 9.
Incorrect
Let the required number of revolutions made by larger wheel be x.
Then, More cogs, Less revolutions (Indirect Proportion)
14 : 6 :: 21 : x 14 x x = 6 x 21
x = 6 x 21 14 x = 9.

Question 20 of 25
20. Question
1 pointsIf 7 spiders make 7 webs in 7 days, then 1 spider will make 1 web in how many days? Correct
Let the required number days be x.
Less spiders, More days (Indirect Proportion)
Less webs, Less days (Direct Proportion)
Spiders 1 : 7 :: 7 : x Webs 7 : 1 1 x 7 x x = 7 x 1 x 7
x = 7.
Incorrect
Let the required number days be x.
Less spiders, More days (Indirect Proportion)
Less webs, Less days (Direct Proportion)
Spiders 1 : 7 :: 7 : x Webs 7 : 1 1 x 7 x x = 7 x 1 x 7
x = 7.

Question 21 of 25
21. Question
1 pointsA flagstaff 17.5 m high casts a shadow of length 40.25 m. The height of the building, which casts a shadow of length 28.75 m under similar conditions will be:
Correct
Let the height of the building x metres.
Less lengthy shadow, Less in the height (Direct Proportion)
40.25 : 28.75 :: 17.5 : x 40.25 x x = 28.75 x 17.5
x = 28.75 x 17.5 40.25 x = 12.5
Incorrect
Let the height of the building x metres.
Less lengthy shadow, Less in the height (Direct Proportion)
40.25 : 28.75 :: 17.5 : x 40.25 x x = 28.75 x 17.5
x = 28.75 x 17.5 40.25 x = 12.5

Question 22 of 25
22. Question
1 pointsIn a camp, there is a meal for 120 men or 200 children. If 150 children have taken the meal, how many men will be catered to with remaining meal?
Correct
There is a meal for 200 children. 150 children have taken the meal.
Remaining meal is to be catered to 50 children.
Now, 200 children 120 men.
50 children 120 x 50 = 30 men Incorrect
There is a meal for 200 children. 150 children have taken the meal.
Remaining meal is to be catered to 50 children.
Now, 200 children 120 men.
50 children 120 x 50 = 30 men 
Question 23 of 25
23. Question
1 pointsAn industrial loom weaves 0.128 metres of cloth every second. Approximately, how many seconds will it take for the loom to weave 25 metres of cloth? Correct
Le the required time be x seconds.
More metres, More time (Direct Proportion)
0.128 : 25 :: 1 : x 0.128x = 25 x 1
x = 25 = 25 x 1000 0.128 128 x = 195.31.
Required time = 195 sec (approximately).
Incorrect
Le the required time be x seconds.
More metres, More time (Direct Proportion)
0.128 : 25 :: 1 : x 0.128x = 25 x 1
x = 25 = 25 x 1000 0.128 128 x = 195.31.
Required time = 195 sec (approximately).

Question 24 of 25
24. Question
1 points36 men can complete a piece of work in 18 days. In how many days will 27 men complete the same work?
Correct
Let the required number of days be x.
Less men, More days (Indirect Proportion)
27 : 36 :: 18 : x 27 x x = 36 x 18
x = 36 x 18 27 x = 24.
Incorrect
Let the required number of days be x.
Less men, More days (Indirect Proportion)
27 : 36 :: 18 : x 27 x x = 36 x 18
x = 36 x 18 27 x = 24.

Question 25 of 25
25. Question
1 points4 matweavers can weave 4 mats in 4 days. At the same rate, how many mats would be woven by 8 matweavers in 8 days?
Correct
Let the required number of bottles be x.
More weavers, More mats (Direct Proportion)
More days, More mats (Direct Proportion)
Wavers 4 : 8 :: 4 : x Days 4 : 8 4 x 4 x x = 8 x 8 x 4
x = (8 x 8 x 4) (4 x 4) x = 16.
Incorrect
Let the required number of bottles be x.
More weavers, More mats (Direct Proportion)
More days, More mats (Direct Proportion)
Wavers 4 : 8 :: 4 : x Days 4 : 8 4 x 4 x x = 8 x 8 x 4
x = (8 x 8 x 4) (4 x 4) x = 16.
good