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Chain Rule - Quantitative Aptitude - Aptitude question and answers
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Chain rule

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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 extent.

Example: Cost is directly proportional to the number of articles. (More Articles, More Cost)

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.

Example: The time taken by a car is covering a certain distance is inversely proportional to the speed of the car. (More speed, less is the time taken to cover a distance).

Note: In solving problems by chain rule, we compare every item with the term to be found out

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Chain rule - Question and Answers

Question 1
If 36 men can do a piece of work in 25 hours, in how many hours will 15 men do it?
A
20 hours
B
60 hours
C
80 hours
D
70 hours
Question 1 Explanation: 
Let the required number of hours be x.
Less man, more hours (indirect proportion)
15:36:: 25: x
15 * x = 36 * 25
X= (36 *25) / 15 = 60 hours
Hence 15 men’s can do it in 60 hours
Question 2
If the wages of 6 men for 15 days be Rs.2100, then the wages of 9 men for 12 days?
A
Rs. 2520
B
Rs. 3065
C
Rs. 7658
D
Rs 2765
Question 2 Explanation: 
Let the required wages be x  More men, more wages( Direct proportion)  Less days, Less wages ( Direct proportion)  Men = 6:9 ::2100 😡  Days = 15:12 :: 2100 : x  (6*15*x) = (9* 12* 2100)  X = [(9*12*2100) / (6* 15)]  X = 420 * 6  X= 2520  Hence, the required wages are Rs. 2520
Question 3
8 children and 12 men complete a certain piece of work in 9 days. If each child takes twice the time taken by a man to finish the work, in how many days will 12 men finish the same work?
A
16 days
B
12 days
C
22 days
D
26 days
Question 3 Explanation: 
2 children = 1 man  (8 children + 12 men) = 16 men  Less men, more days( Indirect proportion )  12 : 16 :: 9: x  12x= (16*9)  12x = 144  X= 144/12  X= 12 days
Question 4
Running at the same constant rate, 6 identical machines can produce a total of 270 bottles per minutes. At this rate, how many bottles could 10 such machines produce in 4 minutes?
A
1500
B
1600
C
1800
D
1964
Question 4 Explanation: 
Let the required number of bottles be x More machines, more bottles(direct proportion) Machines = 6: 10 ::270 : x Time(in minutes) = 1:4 :: 270 : x 6 * 1* x= 10* 4* 270 X= (10*4*270) / (6*1) = 20 * 90 X = 1800
Question 5
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?
A
16
B
17
Hint:
C
19
D
64
Question 5 Explanation: 
Let the required number of mats be x  More mat weavers, more mats(Direct proportion)  More days, more mats ( Direct proportion)  Mat weavers = 4:8 :: 4 : x  Days = 4:8 :: 4:x  4*4*x=8*8*4  X= (8*8*4) / (4*4)  X= 2*2*4  X= 16
Question 6
If a quarter kg of potato coasts 60 paise, how many paise will 200 gm cost?
A
87
B
56
C
48
D
65
Question 6 Explanation: 
Let the required weight be x kg  Less weight, less cost (Direct proportion)  250 : 200 :: 60 : x  250 * x = (200 * 60)  X= (200 * 60) / 250  X= 8*6  X= 48
Question 7
In a hospital there is a consumption of 1350 liters of milk for 70patients for 30 days. How many patients will consume 1710 litres of milk in 28 days?
A
100 patients
B
120 patients
C
95 patients
D
140 patients
Question 7 Explanation: 
Let the required number of number be x = More liters, more patients (Direct proportion) =Less days, more patients (Indirect proportion) Litres = 1350: 1710: : 70 : x Days = 20: 8::70: x  X= (1710*30*70) / (1350 * 28)  = 19 * 5  95 patients
Question 8
39 person can repair a road in 12 days, working 5 hours a day. In how many days will 30 persons, working 6 hours day, complete the work?
A
13 days
B
27 days
C
17 days
D
18 days
Question 8 Explanation: 
Let the required number of days be x  Less persons, More days(Indirect proportion)  More working hours per day, Less days(Indirect proportion)  Person = 30:39 ::12 : x  Working hours/days = 6: 5 ::12 : x  (30*6*x)= (39*5*12)  X= (39*5*12) / (30*6)  X= 13 days
Question 9
If 20 men working together can finish a job in 20 days, then the number of days taken by 25 men of the same capacity to finish the job is?
A
25
B
16
C
20
D
12
Question 9 Explanation: 
25:20:: 20: x or 25x= 20 * 20 Or = [20*20/25] = 16 Required number of days = 16
Question 10
If 16 men working 7 hours day can plough a field in 4l days, in how many days will 14 men working 12 hours clay plough the same field?
A
46
B
32
C
35
D
30
Question 10 Explanation: 
(Men 14:16): (Hrs/Day 12: 7) :: 48 : x 14*12* x = 16* 7 * 48 or x= 32
Question 11
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?
A
6 days
B
12 days
C
3 days
D
4 days
Question 11 Explanation: 
(Men 2x: x): (work 1:1/2):: 12 :y 2x *1 * y = x* ½ *12 or y = 3
Question 12
A wheel rotates 10 times every minute and moves 20 cm during each rotation. How many ends does the wheel move in 1 hour?
A
2000
B
1200
C
600
D
12000
Question 12 Explanation: 
Answer: Option C Number of wheel moves in 1 hour = 10 * 60 = 600 Distance moved = 600 * 200 = 12000
Question 13
If 10 men’s can reap a field in 8 days, then 8 men will reap the same field in?
A
5 days
B
4 days
C
10 days
D
20 days
Question 13 Explanation: 
8: 10 :: 8: x Or 8x = 10 * 8 Or x= 10 Required number of days 10
Question 14
If 18 persons can build a wall 140m long in 42 days, the number of days that 30 persons will take to complete a similar wall 100 m long, is?
A
18
B
24
C
21
D
28
Question 14 Explanation: 
(Length 140:100) : (Persons 30:18) : : 42 : x 140 * 30 * x = 100 * 18 * 42 Or x= 18
Question 15
The price of 438 oranges is Rs. 1384.08. What will be the approximate price of 8 dozens of oranges?
A
300
B
400
C
500
D
250
Question 15 Explanation: 
438:96:: 1384.08 : x Or x= 96 * 1384.08 / 438 = 303.36 Approx cost = Rs. 300
Question 16
If 12 carpenters, working 6 hours a day can make 460 chairs in 24 days, how many chairs will 18 carpenters make in 36 days, each working 8 hours a day?
A
1260
B
920
C
1320
D
1380
Question 16 Explanation: 
(Carpenters 12:18) : (His/Day 6:8) : (Days 24: 36) :: 460 : x 12*6 * 24*x = 18 * 8* 36* 460 Or x= 1380
Question 17
The price of 357 mangoes is Rs. 1517.25. What will be the approximate price of 49 dozen of such mangoes?
A
Rs. 3000
B
Rs. 4000
C
Rs. 3500
D
Rs. 2500
Question 17 Explanation: 
More mangoes, more cost (Direct) 357: 49 * 12:: 1517.25 : x Or 375* x= 49 * 12 * 1517.25 49* 12 * 15|7.25 / 357 = 2499 Approximate cost = Rs. 2500
Question 18
If 15 toys cost Rs. 234, what do 35 toys cost?
A
486
B
546
C
626
D
686
Question 18 Explanation: 
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
Question 19
If 36 men can do a piece of work in 25 hours, in how many hours will 15men do it?
A
40 hrs
B
50 hrs
C
60 hrs
D
70 hrs
Question 19 Explanation: 
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
Question 20
If the wages of 6 men for 15 days be Rs. 200, then the wages of for 12 days?
A
2200
B
2520
C
2720
D
3000
Question 20 Explanation: 
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 (16 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
Question 21
If 20 men can build a wall 66 meters long in 6 days, what length of a similar can be built by 86men in 8 days?
A
44 m
B
49 m
C
54 m
D
59 m
Question 21 Explanation: 
Let the required length be x meters 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 3x 56) X= (35 x 3x 56) / 120 = 49 Hence, the required length is 49 m
Question 22
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?
A
19
B
12
C
15
D
18
Question 22 Explanation: 
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, the required number of days = 15
Question 23
If 7 spiders make 7 webs in 7 days, then 1 spider will make 1 web in how many days?
A
1
B
3
C
7
D
14
Question 23 Explanation: 
Answer: Option C Let the required number days be x Less spider, More days (Indirect proportion) Less webs, less days (Direct Proportion) 1 x7 x X = 7 x 1 x 7  X = 7
Question 24
If 9 engines consume 24 metric 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?
A
22 metric tonnes
B
24 metric tonnes
C
26 metric tonnes
D
28 metric tonnes
Question 24 Explanation: 
Let 3engines 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 proportion) Number of engines 9:8 Working hours 8: 13:: 24 : x Rate of consumption (1/3) : (1/4) [9x8x(1/3)x X] = (8 x 13 x (1/4) x 24) 24x = 624 X= 26 Hence, the required consumption of coal= 26metric tonnes
Question 25
A garrison of 3300 men had provisions for 32 days, when given at the rate of 860 gms per head. At the end of 7 days, reinforcement arrives and it was for that the provisions will last 17 days more, when given at the rate of 826 gms per head, what is the strength of the reinforcement?
A
1500
B
1700
C
1900
D
2100
Question 25 Explanation: 
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) Ratio 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
Question 26
36 men can complete a piece of work in 18 days. In how many days will 27 men complete the same work?
A
12
B
18
C
22
D
24
Question 26 Explanation: 
Let the required number of days be x Less man, more days (Indirect proportion) 27 :36 ::18 : x  27 X x = 36 x X =36 x 18/27 X= 24
Question 27
If a quarter kg of potato costs 60 paise, how many paise will 200 gm cost?
A
48 paise
B
54 paise
C
56 paise
D
72 paise
Question 27 Explanation: 
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 28
If cost of x meters of wire is d rupees, then what is the cost of y meters of wire at the same rate?
A
Rs. (xy/d)
B
Rs. (xd)
C
Rs.(yd)
D
Rs. (yd/x)
Question 28 Explanation: 
Cost of x meter = Rs. d Cost of 1 meter = Rs.(d/x) Cost of y meters = Rs.[(d/x).y] = Rs.(yd/x)
Question 29
39 Persons can repair a road in 12 days, working 5 hours day. In how many days will 30 persons, working 6 hours a day, complete the work?
A
10
B
13
C
14
D
15
Question 29 Explanation: 
Let the required number of days be x Less persons, more days (Indirect proportion) More working hours per day, less days (Indirect proportion) 30 x 6 x X = 39 x 5 x12 X= 13
Question 30
In a cam, 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?
A
50
B
40
C
30
D
20
Question 30 Explanation: 
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 = 30 men
Question 31
A contractor undertakes to do a piece of work in 40 days. He engages 100 men at the beginning and 100 more after 35 days and completes the work in stipulated time. If he had not engaged the additional men, how many days behind schedule would it be finished?
A
3
B
5
C
6
D
9
Question 31 Explanation: 
4500 men can finish the work in 1day. 100 men can finish it in = 45 days This is 5 days behind schedule
Question 32
If a cloth merchant sells ‘a’ meter of cloth for Rs.x, then what is the selling price of ‘b’ meters of cloth?
A
Rs.(b*x)
B
Rs. {(b*x)/a}
C
Rs.{(a*b)/x}
D
none of these
Question 32 Explanation: 
Cost of ‘a’ meters of cloth = Rs. x Therefore, each meter of cloth costs Rs. (x/a). The cost of ‘b’ meters of cloth = Rs. b*(x/a) = Rs. {(b*x)/a}
Question 33
A military camp has a food reserve for 250 personnel for 40 days. If after 15 days 50 more personnel are added to the camp, find the number of days the reserve will last for?
A
20
B
36
C
25
D
42
Question 33 Explanation: 
As the camp has a reserve for 250 personnel that can last for 40 days, after 10 days the reserve left for 250 personnel is for 30 days. Now 50 more personnel are added in the camp. hence, the food reserve for 300 personnel will last for: 250:300:: x:30 ...(It is an indirect proportion as less men means more days) X= (250*30)/300 X= 25 days
Question 34
A group of 55 adults and 70 children go for trekking. If there is meal for either 70 adults or 90 children and if 28 adults have their meal, find the total number of children that can be catered with the remaining food.
A
42
B
54
C
90
D
70
Question 34 Explanation: 
As there is meal for 70 adults and 28 have their meal, the meal left can be catered to 42 adults. Now, 70 adults = 90 children 7 adult = 9 children Therefore, 42 adults = 54 children Hence, the meal can be catered to 54 children
Question 35
If a carpenter completes 3/8th of his work in 6 days, then how many more days will he require completing his remaining work?
A
10
B
12
C
6
D
16
Question 35 Explanation: 
As 3/8th of the work is completed, the work remaining is 58th of the total. (3/8):6:: (5/8):x X= 6*(5/8) / (3/8) X= 10
Question 36
If a certain number of people can dig earth 100m deep, 25m long, and 30m broad in 12days, then find the number of people will required to dig earth 75m deep, 20m long and 50m broad?
A
12
B
18
C
6
D
1
Question 36 Explanation: 
More number of days means – more length, more depth and more width. Hence it’s a direct proportion. (100*25*30): (75*20*50):: 12 😡 75000:75000:: 12:x X = 12
Question 37
For a road work, a contractor was given a deadline to complete the work in 25 days. Hence, he employed a certain number of workers to accomplish the job. But from the very first day 9 workers were absent and the remaining workers could finish the work in 40 days. What number of workers did the contractor hired in the beginning?
A
20
B
30
C
24
D
16
Question 37 Explanation: 
Let the number of workers initially hired be x Hence, x workers can complete the work in 25 days and (x-9) workers can complete the work in 40 days Now, the number of men and the amount of work are in direct proportion and number of men and number of days in indirect proportion X*25 = (x -9)*40 25x=40x – 360 15x=360 X=24
Question 38
If 10 men can do a certain amount of work in 24days, then in how many days can 20 men complete half the amount of work?
A
12
B
24
C
6
D
18
Question 38 Explanation: 
M1D1W2 = M2D2W1 10*24*W1/2 = 20* D2*W1...... (W2=W1 / 2) D2 = 6 days
Question 39
In how many days can 4 men and 4 women complete a certain work, if 2 men or 6 women can complete the same work in 12days?
A
4.5
B
6
C
12
D
4
Question 39 Explanation: 
2men = 6women Hence, 4 men = 12 women 4 men and 4 women = 12 + 4 = 16 women M1 D1 W2= M2 D2 W1 M1 D1 = M2 D2 ....(W1 = W2) 6*12 = 16*D2 D2 = 4.5 day
Question 40
A two stored building is to be completed in 48 days. To meet the deadline 54 men were employed and were made to work for 10 hours a day. After 30 days 5/9th of the work was completed. How many more workers should be employed to meet the deadline if each workers are now made to work 8 hours a day?
A
36
B
90
C
40
D
50
Question 40 Explanation: 
54men work 10 hours a day for 30 days and 5/9th of the work is completed Now, let x workers be employed to work 8 hours a day for the rest 18 days to complete 4/9th of the work M1 D1 T1 W2 = M2 D2 T2 W1 54*30*10*4/9 = x*18* 8*5/9 X= 90 Hence, 36 more workers should be employed
Question 41
If the cost of x meters of wire is d rupees, then what is the cost of y meters of wire at the same rate?
A
Rs. (xd/y)
B
Rs. xd
C
Rs.(yd/x)
D
Rs. yd
Question 41 Explanation: 
Cost of x meters of wire = Rs. d Cost of 1 meter of wire= Rs.(d/x) Cost of y meter of wire = Rs. (y*dx) = Rs. (yd/x)
Question 42
In 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?
A
50
B
30
C
40
D
10
Question 42 Explanation: 
Meal for 200 children = Meal for 120 men Meal for 1 child = Meal for 120/200 men Meal for 150 children = Meal for 120 x 150/200 men = Meal for 90 men Total meal available = meal for 120 men Remaining meal = Meal for 120 men – Meal for 90 men = Meal for 30 men
Question 43
If a quarter kg of potato costs 60 paise, how many paise dos 200 gm cost/
A
65 paise
B
70 paise
C
52 paise
D
48 paise
Question 43 Explanation: 
Let 200 gm potato costs x paise Cost of ¼ kg potato = 60 paise  Cost of 250gm potato = 60 paise  More quantity, more prise  Hence we can write as  Quality(200:250)::x:60  200 x 60 = 250 x X  4 x 60 = 5 x X  4 x 12 = X  X= 48
Question 44
A wheel that has 6 cogs is meshed with a large wheel of 14 cogs. If the smaller wheel has made 21 revolutions, what will be the number of revolutions made by the large wheel?
A
15
B
12
C
21
D
9
Question 44 Explanation: 
Let the number of revolutions made by the larger wheel be x More cogs, less revolutions (indirect proportion) Hence we can write as Cogs(6:14)::x:21  6 x 21 = 14 x X  6 x 3 = 2 x X  3 x 3 = X  X= 9
Question 45
A certain industrial loom weaves 0.128 meters of cloth every second. Approximately how many seconds will it take for the loom to weave 25 meters of cloth?
A
205
B
200
C
195
D
190
Question 45 Explanation: 
Let the required number of second be x More cloth, more time,(direct proportion) Hence we can write as Cloth 0.128:25}:: 1: x  0.128x= 25  X= 25/128 = 25000/128  = 3125/16 = 195
Question 46
21 goats eat as much as 15 cows. How many goats eat as much as 35 cows?
A
49
B
36
C
50
D
41
Question 46 Explanation: 
15 cows = 21 goats 1 cow = 21/15 goats 35 cows = 21 x 35/15 goats = 21 x 7/3 goats = 7 x 7 goats = 49 goats
Question 47
A flagstaff 17.5 m high casts a shadow of length 40.25m.what will be the height of a building, which casts a shadow of length 28.75m under similar conditions?
A
12.5 m
B
10.5 m
C
14
D
12
Question 47 Explanation: 
Let the required height of the building be x meter More shadow length, more height Hence we can write as Shadow length {40.25:28.75}:: 17.5 : x  40.25x X = 28.75 x 17.5  X= 28.75 x17.5/40.25  2875 x 7/1610  2875/230  575/46  12.5
Question 48
A fort had provision of food for 150 men for 45 days. After 10 days, 25 men left the fort. Find out the number of days for which the remaining food will last?
A
44
B
42
C
36
D
52
Question 48 Explanation: 
Given that the fort had provision of food for 150 men for 45 days Hence, after 10 days, the remaining food is sufficient for 150 men for 35 days Remaining men after 10 days =150 – 25 = 125 Assume that after 10 days, the remaining food is sufficient for 125 men for x days More men, less days  Men {150:125}:: x:35  150 x 35 = 125x=> 6x35= 5x=>x = 6x7 = 42  The remaining food is sufficient for 125 men for 42 days
Question 49
14 pumps of equal capacity can fill a tank in 6 days. If the tank has to be filled in 4 days, the number of extra pumps need is?
A
7
B
21
C
14
D
28
Question 49 Explanation: 
The total volume of the tank is constant. The volume of water which one pump supplies in one day is constant. As more pumps are used the time to fill the tank will decrease 4:6:: 14: x Or 4x = 6*14 Or x= 6*14/4 = 21 Extra pumps needed = (21-14) = 7
Question 50
In a dairy farm, 40 cows eat 40 bags of husk in 40 days. How many days one cow will eat one bag of husk?
A
1
B
40
C
26
D
20
Question 50 Explanation: 
Assume that in x days, one cow will eat one bag of husk. Less cows, more days Less bags, less days Hence, we can write as [Cow 1:40 bags 40:1] 1 x 40 * x = 40*1 * 40 X= 40
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