Chain Rule

Solution

Let the required quantity be x kg.Then

more days ,more cost ( direct proportion)

7:58::105:x

7x=58×105

x=58×105/7=870 kg

Hence the canteen will require 870kg of wheat for 58 days

Solution

Let the required number of hours be x Then,

less men,more hours(indirect proportional)

15:36::25:x

(15x){(36×25)

x=36×25/15=60

Solution

Let the required number of women be x Then,

more days,less woman(indirect proportional)

25:15::35:x

25x=15×35

x=15×35/25

x=21

Hence 21 women can do the work in 25 days

Solution

originally let there be x people

less people,more days ( indirect proportional)

(x-9):x::24:32

(x-9)×32=x×24

8x=288

x=36

Hence 36 people were supposed to be working originally

Solution

Let the required number of days be x

more students,less days(indirect proportional)

more pencils,more days(direct proportional)

students 15:5::9:x

pencils 18:66::9:x

(15×18×x)=(5×66×9)

x=5×66×9/15×18

x=11

Hence the required number of days is 11

Solution

Let the required length be x metres

More men ,more length built(direct proportional)

Less days,less length built (direct proportional)

men 20:35::56:x

Days 6:3::56:x

20×6x=35×5×56

x=35×3×56/120=49

Hence the required length is 49 m

Solution:

Let the required number of days be x

Less men,more days(indirect proportional)

more hours per day ,less days(indirect proportional)

men 7:8::20:x

hours per day 10:9::20:x

(7×10x)=8×9×20

x=8×9×20/7×10

x=144/7

Hence required number of days =144/7

Solution:

Let the required number of days be x

12 men=18 women

8 men =(18/12)×8 women=12 women

more women,less days (indirect proportional)

28:18::14:x

28x=18×14

x=18×14/28

x=9

Hence required number of days=9

Solution:

Let the required number of days be x

13 men=18 women

8 men =(18/13)×8 women=11 women

more women,less days (indirect proportional)

27:18::14:x

27x=18×14

x=18×14/27

x=28/3

Hence required number of days=28/3

solution:

let the required the number of days be x

less person,more days( indirect proportional)

less hours ,more days(indirect proportional)

more works more days( direct proportional)

persons 14:15::21:x

hours per day 6:8::21:x

work y:3/2y::21:x 14×6yx=15×8×3/2y×21

x=15×8×3y×21/2×14×6y

x=45

Solution:

Let the distance in the two cases be y and 2y respectively and the speed be z and 2z respectively.Let the required number of days be x.

more distance,more days(Direct proportional)

More speed ,less days(indirect proportional)

more resting,more days.(Direct proportional)

Distance y:2y::40:x

speed 2z:z::40:x

Resting time 9:18::40:x

y×2z×9x=2yz×18×40

x=2yz×18×40/y×2z×9

x=80

Hence the required number of days=80

Output: Chaminda vaas holds the record Of best bowling performance in ODI's.He Took 8for 19 against Zimbabwe in December 2001.

cost of x metre =d.

cost of 1metre=d/x

cost of y metres=d/x×y

=yd/x

5.5 dozen pens=(5.5×12)pens=66 pens .Let the cost of 16 pens be x

less pens,less cost(direct proportional)

66:16::1287:x

66x=16×1287

x=16×1287/66=312

let the required price be x

more mangoes,more price (direct proportional)

357:(49×12)::1517.25:x

357x=49×12×1517.25

x=(49×12×1517.25)/357

x=2499

hence the approximate price is 2500

solution

le the required cost be x paise

less weight,less cost (Direct proportional)

250:200::60:x

250×x=(200×60)

x=200×60/250

x=48

solution

let the actual distance be x km.then,

more distance,more actual distance (direct proportional)

0.6:80.5::6.6:x

0.6x=80.5×6.6

x=80.5×6.6/0.6

x=885.5

le the required weight be x kg then,

less length less weight (direct proportional)

11.25:6::42.75:x

11.25×x=6×42.75

x=6×42.75/11.25

x=22.8

Solution

le the required tume be x second

more meters ,more time(direct proportional)

0.128:25::1:x

0.128×x=25×1

x=80.5×6.6/0.6

solution:

e tablespoon=1 tablespoon

3/2teaspoon=½table spoon

let the number of tablespoon required be x.

more people,more salt (direct proportional)

4:18::½:x

4x=18×½=9

x=9/4=2.25

le the dimensions of the shorter side be x

more is the longer side,more is the shorter side (direct proportion)

5/2:4::15/8:x

5/2x=4×15/8

x=15/2×2/5

x=3

Solution

total number of days=(30+31+30) =91 days

let the number of bananas be x.

more days,more bananas (direct proportional)

7:91::651:x

7x=91×651

x=91×651/7

x=8463

solution

Remaining part=(1-4/9)=5/9

let the required time be x minutes.

more volume to be filled,more time taken(direct proportion)

4/5:5/9::1:x

4/9x=5/9

x=5/8×9/4=5/4

solution:

5 cm on the map represent 1450km.

1cm on the map represent (1450/5)km=290km

Hence the scale is 1cm :290km i.e;1:29×10⁶cm

let the height of the building be x metres

less length shadow,less is the height (direct proportion)

40.25:28.75::17.5:x

40.25x=28.75×17.5

x=28.75/40.25

x=12.5

solution

let the height of the minar with flagstaff be x metre.More length shadow,more is the height (direct proportional)

24:50::36:x

24x=50×36

x=50×36/24 =75

hence height of the minar=(75-3) =72m

Solution

work done=5/8 . Balance work=1-5/8)=3/8

less work .less days(direct proportional)

let the required number of days be x

then,5/8:3/8::10:x

5/8x=3/8×10

x=3/8×10×8/5

x=6

Solution

let the required number of days be x.Less men,more days (indirect proportion)

42:56::24:x

42x=56×24

x=56×24/42

x=6

Solution

let the required number of men be x.

more days ,less men(Indirect proportion)

20:16::30:x

20x=16×30

x=16×30/20

x=24

Solution

Let the required number of workers originally hired be x.

less workers,more days(indirect proportion)

(x-5):x::10:12

12(x-5)=10x

2x=60

x=30

let the required number of revolution made by larger wheel be x.

Then,more cost,less revolutions. (Indirect proportion)

14:6::21:x

14x=6×21

x=6×21/14

x=9

Solution

there is a meal for 200 children.150 have taken the meal.Remaining meal is to be catered to 50 children.Now ,200 children=120 men

50 children=1201/200×50 men

=30 men

Solution

Let the required cost be x Then,

more packets,more cost (direct proportion.) More weight ,more cost (direct proportion)

packets 16:27::28:x

weight 900:1000::28:x

16×900x=27×1000×28

x=27×1000×28/16×900=105/2=52.50

Solution

Let the number of mats be x.Then, more weavers more mats (direct proportion).More days,more mats(direct proportion)

weavers 4:8::4:x

days 4:8::4:x

4×4x=8×8×4

x=8×8×4/4×4

x=16

Solution

since each maid would work with one mop,so we shall consider 1 maid and q mop as 1 unit. Let the required time be x hours.

less maids and mops ,more time,less time (indirect proportion)

less floors,less time(direct proportion)

maida and mops 3:7::7:x

floors 7:3::7:x

3×7x=7×3×7

x=7×3×7/3×7

x=7