Rule Of Three
Class 8th Mathematics West Bengal Board Solution
- Today my father has bought 15kg. Of rice for Rs. 390. Let’s work out using the Rule of…
- Venkat uncle will make 4 shirts of same size with 20 meters of cloth.Let’s work out…
- It took 15 days for 30 heads of labourers to dig a pond at Bakultala village. Let’s…
- My aunt reached my maternal uncle’s house in five hours by driving the car at a speed…
- There was a stock of food grains for 9 days to cater the needs of 4000 people at a…
- 42 labourers of a farm at Nasibpur village can cultivate the entire land of the farm in…
- It takes 27 days to make 1000 spare parts by 16 numbers of machines. Let’s work out…
- Q8A
- {cc} { (km/hr.) } & { (km) } {9}&{112.5} {12}&{?}
- Q8C
- Q8DLets
- The work for construction of the village road will be started. It has been decided that…
- In a book of 105 pages written by Subhash uncle, there are in average 25 lines in each…
- 540 Bighas of land of an agricultural farm are to cultivated in 14 days.120 Bighas of…
- 30 heads of people repair {3}/{7} part of a road of a village in 15 days. Let’s…
- A pump of 5 HP can lift 36000 litres of water in 8 hours. Let’s work out using the…
- There are two motors of 5 Hp and 3Hp in a factory. The 5 Hp motor requires 20 units of…
- In a loom at Goplanagar 14 weavers can weave 210 sarees in 12 days. The workshop got an…
- A company has got the work of unloading goods from a ship in 10 days. 280 heads of…
- A power-loom is 2 {1}/{4} times more powerful than a hand-loom. 12 hand-looms weave…
- 2400 Bighas of land of Cooperative Society can be cultivated by 25 farmers in 36 days.…
- A ship takes 25 days to sail from Kolkata to Cochin. The ship started with 36 sailors…
- 36 heads of people of a certain village can construct 12- metres of raod working 6…
- 250 heads of people can dig a pond of size 50 meters long, 35 metres wide and 5.2 deep…
- Let’s make mathematical problems with help of given relations and find out their…
- Q14B
Lets Work Out 10.1
Question 1.Today my father has bought 15kg. Of rice for Rs. 390. Let’s work out using the Rule of Three method how much he would require if he would have bought the same quality of 17 kg of rice.
Answer:
theorem1:-
The Rule of Three is a Mathematical Rule that allows you to solve problems based on proportions. By having three numbers: a, b, c,
(a)Direct proportions rule of 3:-
if a
b
c
then 
(b)inverse proportions rule of 3:-
if ab
c then 
method used is called direct proportions method
formula:- (i)direct method----
(ii)indirect or inverse proportions or inverse proportions xy=k
GIVEN :-15 kg of rice cost RS 390
1 kg of rice cost will be
17 kg of rice cost will be
therefore RS 442 will be the cost of 17 kg rice.
Question 2.
Venkat uncle will make 4 shirts of same size with 20 meters of cloth.Let’s work out using the the Rule of Three method how many meters of cloth Venkat uncle will have to purchase for making 12 such shirts.
Answer:
theorem1:-
The Rule of Three is a Mathematical Rule that allows you to solve problems based on proportions. By having three numbers: a, b, c,
(a)Direct proportions rule of 3:-
if ab
c
then
(b)inverse proportions rule of 3:-
if ab
c then
formula:- (i)direct method----
(ii)indirect or inverse proportions xy=k
given:-method used is called direct proportions method
20m of cloth gives 4 shirts
1 shirt will required
12 shirt will required
of cloth
therefore 12 shirt will required 60 m of cloth
Question 3.
It took 15 days for 30 heads of labourers to dig a pond at Bakultala village. Let’s work out using the the Rule of Three method in how many days 25 heads of labourers could have completer the said work.
Answer:
theorem1:-
The Rule of Three is a Mathematical Rule that allows you to solve problems based on proportions. By having three numbers: a, b, c,
(a)Direct proportions rule of 3:-
if ab
c then
(b)inverse proportions rule of 3:-
if ab
c then
formula:- (i)direct method----
(ii)indirect or inverse proportions xy=k
(iiii)d1
t1=d2t2
given:-
method used is called indirect method
d1t1=d2t2
3015=25t2
18=t2
Therefore 25 labourers will work for 18 day
Question 4.
My aunt reached my maternal uncle’s house in five hours by driving the car at a speed of 40 km/hr. Let’s work out using the Rule of Three method how long it would have taken if she would have drives the car at a speed of 50 k.m/hr.
Answer:
theorem1:-
The Rule of Three is a Mathematical Rule that allows you to solve problems based on proportions. By having three numbers: a, b, c,
(a)Direct proportions rule of 3:-
if ab
c then
(b)inverse proportions rule of 3:-
if ab
c then
formula:- (i)direct method----
(ii)indirect or inverse proportions xy=k
method used is called indirect or inverse proportions method
speed of car 40km/hr in 5 hour time
now 50km/hr speed will take time
Therefore 4hr is time take at speed of 50 km/hr to reaches houses
Question 5.
There was a stock of food grains for 9 days to cater the needs of 4000 people at a shelter camp in Mongalpur village. After 3 days 1000 people left the camp for another place. Let’s work out using the Rule of three method in how many days the rest of the people will consume the remaining food grains.
Answer:
theorem1:-
The Rule of Three is a Mathematical Rule that allows you to solve problems based on proportions. By having three numbers: a, b, c,
(a)Direct proportions rule of 3:-
if ab
c then
(b)inverse proportions rule of 3:-
if ab
c then
formula:- (i)direct method----
(ii)indirect or inverse proportions xy=k
given:- method used is called indirect or inverse proportions method
In a shelter camp of 4000 people have food 9 days.
4000× 9 =36,000 ration available
After 3 days 1000 men went away to another place.
in this, 3 days,
4000× 3 = 12000 ration consumed
36000 - 12000 = 24000 ration remain
Let d = no. of days
(4000-1000)d = 24000
3000d = 24000
d=12days
Question 6.
42 labourers of a farm at Nasibpur village can cultivate the entire land of the farm in 24 days. But suddenly 6 labourers became ill during the period of cultivation. Let’s work out using the Rule of three method how many days it will take to cultivate the entire land of the farm by the rest of the labourers.
Answer:
theorem1:- The Rule of Three is a Mathematical Rule that allows you to solve problems based on proportions. By having three numbers: a, b, c,
(a)Direct proportions rule of 3:-
if ab
c then
(b)inverse proportions rule of 3:-
if ab
c then
method used is called indirect or inverse proportions method
formula:- (i)direct method----
(ii)indirect or inverse proportions xy=k
(iii)work done=people x day
given:-
work done=people x day
42x24=1008
again work
work formula=(42-6)xday
1008=36xday
day=28
Question 7.
It takes 27 days to make 1000 spare parts by 16 numbers of machines. Let’s work out using the Rule of Three method how many days will it take to make the same number of spare parts if additional two machines are installed.
Answer:
theorem1:- The Rule of Three is a Mathematical Rule that allows you to solve problems based on proportions. By having three numbers: a, b, c,
(a)Direct proportions rule of 3:-
if ab
c then
(b)inverse proportions rule of 3:-
if ab
c then
formula:- (i)direct method----
(ii)indirect or inverse proportions xy=k
given:-
method used is called indirect or inverse proportions method
work done=no of day x no of spare x no of machine
work done=27x1000x16=432000
work done =432000=no of day x1000x 18
Question 8.
Answer:
theorem1:- The Rule of Three is a Mathematical Rule that allows you to solve problems based on proportions. By having three numbers: a, b, c,
(a)Direct proportions rule of 3:-
if ab
c then
(b)inverse proportions rule of 3:-
if ab
c then
formula:- (i)direct method----
(ii)indirect or inverse proportions xy=k
given:-
method used is called direct method
for 1 pen is 112.5/25= 4.5cost
so,12 pen cost is 4.5x12=54
Question 9.
Answer:
theorem1:-
The Rule of Three is a Mathematical Rule that allows you to solve problems based on proportions. By having three numbers: a, b, c,
(a)Direct proportions rule of 3:-
if ab
c then
(b)inverse proportions rule of 3:-
if ab
c then
formula:- (i)direct method----
(ii)indirect or inverse proportions xy=k
given:-
method used is called direct method
with 9 km/hr velocity 112.25km distance is travelled
with 1 km/hr velocity 112.25/9=12.4722 km distance is travelled
so,with 12km/hr velocity 12.4722x12=149.6666km distance
Question 10.
Answer:
theorem1:-
The Rule of Three is a Mathematical Rule that allows you to solve problems based on proportions. By having three numbers: a, b, c,
(a)Direct proportions rule of 3:-
if ab
c then
(b)inverse proportions rule of 3:-
if ab
c then
formula:- (i)direct method----
(ii)indirect or inverse proportions xy=k
given:- method used is called direct method
6 pump is used for 31.2 of land cultivation
1 pump will be used for
13 pumps will used for cultivation of 13x5.2=67.6 of land
Question 11.
Answer:
theorem1:-
The Rule of Three is a Mathematical Rule that allows you to solve problems based on proportions. By having three numbers: a, b, c,
(a)Direct proportions rule of 3:-
if ab
c then
(b)inverse proportions rule of 3:-
if ab
c then
formula:- (i)direct method----
(ii)indirect or inverse proportions xy=k
given:-
method used is called direct method
425 student required 306gm of grain
1 student need 
of grain
458 no. of student requried
of grain
Lets Work Out 10.2
Question 1.The work for construction of the village road will be started. It has been decided that 14 people will work 4 hours daily for 15 days to complete the total work. Let’s work out using the Rule of three method how long it will take to complete the work by 24 people working 7 hours daily.
Answer:
theorem1:-
The Rule of Three is a Mathematical Rule that allows you to solve problems based on proportions. By having three numbers: a, b, c,
(a)Direct proportions rule of 3:-
if ab
c then
(b)inverse proportions rule of 3:-
if ab
c then
formula:- (i)direct method----
(ii)indirect or inverse proportions xy=k
given: -
method used is called indirect or inverse proportions method
work done=people x hour x day
=14x4x15=840
for same work done
840=people x hour x day
840=24x7xday
day=5
Question 2.
In a book of 105 pages written by Subhash uncle, there are in average 25 lines in each page and there are in average 8 words in each line. Let’s work out using the method of the Rule of Three how many pages will be there in the book if there are 30 lines in each page having 10 words in each line.
Answer:
theorem1:-
The Rule of Three is a Mathematical Rule that allows you to solve problems based on proportions. By having three numbers: a, b, c,
(a)Direct proportions rule of 3:-
if ab
c then
(b)inverse proportions rule of 3:-
if ab
c then
formula:- (i)direct method----
(ii)indirect or inverse proportions xy=k
given:-
method used is called indirect or inverse proportions method
book content =no. of page x no. of line x no .of word
=105x25x8=21000
again
book content =no. of page x no. of line x no .of word
21000=no. of page x30x10
no.of page =70.
Question 3.
540 Bighas of land of an agricultural farm are to cultivated in 14 days.120 Bighas of land was cultivated in first 4 days by 5 tractors of equal strength. Let’s work out using the method of the Rule of Three how many tractors will be required to complete the cultivation in time.
Answer:
theorem1:-
The Rule of Three is a Mathematical Rule that allows you to solve problems based on proportions. By having three numbers: a, b, c,
(a)Direct proportions rule of 3:-
if ab
c then
(b)inverse proportions rule of 3:-
if ab
c then
formula:- (i)direct method----
(ii)indirect or inverse proportions xy=k
given:-
method used is called indirect or inverse proportions method
w1=540,w2=120,d1=14,d2=4,t1=?,t2=5
t1=6.42
Question 4.
30 heads of people repair 
part of a road of a village in 15 days. Let’s work out using the method of the Rule of Three how many days it will take to repair the rest of the road if additional 10 heads of people join.
Answer:
theorem1:-
The Rule of Three is a Mathematical Rule that allows you to solve problems based on proportions. By having three numbers: a, b, c,
(a)Direct proportions rule of 3:-
if ab
c then
(b)inverse proportions rule of 3:-
if ab
c then
formula:- (i)direct method----
(ii)indirect or inverse proportions xy=k
given:-w1=3/7,w2=4/7,d1=15,d2=?,p1=30,p2=40
d2=15
Question 5.
A pump of 5 HP can lift 36000 litres of water in 8 hours. Let’s work out using the method of the Rule of Three how long it will take to lift 63000 litres of water by a 7 HP pump.
Answer:
formula:-
theorem1:-
The Rule of Three is a Mathematical Rule that allows you to solve problems based on proportions. By having three numbers: a, b, c,
(a)Direct proportions rule of 3:-
if ab
c then
(b)inverse proportions rule of 3:-
if ab
c then
(i)direct method----
(ii)indirect or inverse proportions xy=k
given:-method used is called indirect or inverse proportions method
w1=5,w2=7,l1=36000,l2=63000,h1=8,h2=?
h2=6.4 hr
Question 6.
There are two motors of 5 Hp and 3Hp in a factory. The 5 Hp motor requires 20 units of electricity in 8hours. Let’s work out using the method of the Rule of Three how many units of electricity will be required if the 3Hp motor works for 10 hours.
Answer:
theorem1:-
The Rule of Three is a Mathematical Rule that allows you to solve problems based on proportions. By having three numbers: a, b, c,
(a)Direct proportions rule of 3:-
if ab
c then
(b)inverse proportions rule of 3:-
if ab
c then
formula:- (i)direct method----
(ii)indirect or inverse proportions xy=k
given:- method used is called indirect or inverse proportions method
w1=5,w2=3,u1=20,t1=8,t2=10
u2=9.6 unit
Question 7.
In a loom at Goplanagar 14 weavers can weave 210 sarees in 12 days. The workshop got an order to supply 300 sarees within 10days during the Pujas. Let’s work out using the method of the Rule of Three how many extra weavers have to be employed to complete the work in time.
Answer:
theorem1:-
The Rule of Three is a Mathematical Rule that allows you to solve problems based on proportions. By having three numbers: a, b, c,
(a)Direct proportions rule of 3:-
if ab
c then
(b)inverse proportions rule of 3:-
if ab
c then
formula:- (i)direct method----
(ii)indirect or inverse proportions xy=k
given:- method used is called indirect or inverse proportions method
s1=210,s2=200,w1=14,d1=12,d2=10,w1=?
w2 =24
that mean 24-14=10 more people are required.
Question 8.
A company has got the work of unloading goods from a ship in 10 days. 280 heads of people have been employed for this purpose After 3 days it is seen that 
th of the work has been completed. Let’s work out using the method of the Rule of Three how many heads of people are to be engaged to complete the work in time.
Answer:
theorem1:-
The Rule of Three is a Mathematical Rule that allows you to solve problems based on proportions. By having three numbers: a, b, c,
(a)Direct proportions rule of 3:-
if ab
c then
(b)inverse proportions rule of 3:-
if ab
c then
formula:- (i)direct method----
(ii)indirect or inverse proportions xy=k
given:-
method used is called indirect or inverse proportions method
w1=w,
,
p1=?,p2=280,d1=10,d2=3
p1=336
Question 9.
A power-loom is 
times more powerful than a hand-loom. 12 hand-looms weave 1080 meters length of cloth in 18 days. Let’s work out by the Rule of Three how many power-looms will be required to weave 2700 meters length of cloth in 15 days.
Answer:
theorem1:-
The Rule of Three is a Mathematical Rule that allows you to solve problems based on proportions. By having three numbers: a, b, c,
(a)Direct proportions rule of 3:-
if ab
c then
(b)inverse proportions rule of 3:-
if ab
c then
formula:- (i)direct method----
(ii)indirect or inverse proportions xy=k
GIVEN:-
method used is called direct proportions method
So number of looms = 
Q=25.92
Question 10.
2400 Bighas of land of Cooperative Society can be cultivated by 25 farmers in 36 days. It was seen that half of the land of the Society could cultivate in 30 days after purchasing a tractor. Let’s work out the power of a tractor equivalent to the number of farmers using the method of Rule of Three.
Answer:
theorem1:-
The Rule of Three is a Mathematical Rule that allows you to solve problems based on proportions. By having three numbers: a, b, c,
(a)Direct proportions rule of 3:-
if ab
c then
(b)inverse proportions rule of 3:-
if ab
c then
formula:- (i)direct method----
(ii)indirect or inverse proportions xy=k
GIVEN:-method used is called indirect or inverse proportions method
w1=2400,w2=1200,p1=25,p2=?,d1=36,d2=30
p2=15
therefore 15 farmer power equal to power of 1 tractor
Question 11.
A ship takes 25 days to sail from Kolkata to Cochin. The ship started with 36 sailors for each of which 850 gm of food was allotted. But the ship rescued 15 sailors from anothersinking-ship after 13 days of journey and the ship reached Cochin in 10 days increasing the speed. Let’s work out using the method of the Rule of Three what will be the quantity of food to be consumed by of each sailor to each Cochin safely and the entire storage of food would be consumed by this time.
Answer:
theorem1:-
The Rule of Three is a Mathematical Rule that allows you to solve problems based on proportions. By having three numbers: a, b, c,
(a)Direct proportions rule of 3:-
if ab
c then
(b)inverse proportions rule of 3:-
if ab
c then
formula:-
(i)direct method----
(ii)indirect or inverse proportions xy=k
As number of sailors increases quantity of food decrease.
Hence inverse proportion is used:
Food available is =
= 780 gm
Question 12.
36 heads of people of a certain village can construct 12- metres of raod working 6 hours daily in 12 days. Another 6 heads of people are involved in this work and the duration of work of each day is increased by 2 hours. Let’s work out using the method of the Rule of Three the length of road to be constructed in 9 days.
Answer:
theorem1:-
The Rule of Three is a Mathematical Rule that allows you to solve problems based on proportions. By having three numbers: a, b, c,
(a)Direct proportions rule of 3:-
if ab
c then
(b)inverse proportions rule of 3:-
if ab
c then
formula:- (i)direct method----
(ii)indirect or inverse proportions xy=k
GIVEN:-
method used is called indirect or inverse proportions method
m1=12, m2=? ,p1=36,p2=42,h1=6,h2=8,d1=12,d2=9
m2 =14 m
Question 13.
250 heads of people can dig a pond of size 50 meters long, 35 metres wide and 5.2 deep in 18 days by working 10 hours daily.Let’s work out using the method of the Rule of Three how many days it will take for 300 people to dig a pond of size 65 metres long, 40 metres wide and 5.6 metres deep by working 8 hours daily.
Answer:
theorem1:- The Rule of Three is a Mathematical Rule that allows you to solve problems based on proportions. By having three numbers: a, b, c,
(a)Direct proportions rule of 3:-
if ab
c then
(b)inverse proportions rule of 3:-
if ab
c then
formula:- (i)direct method----
(ii)indirect or inverse proportions xy=k
GIVEN:-method used is called indirect or inverse proportions method
v1=5
,
v2 =65
,
p1=250,p2=300,d1=18,d2=?,h1=10,h2=8
d2=30
Question 14.
Let’s make mathematical problems with help of given relations and find out their solutions by the Rule of Three-
Answer:
theorem1:- The Rule of Three is a Mathematical Rule that allows you to solve problems based on proportions. By having three numbers: a, b, c,
(a)Direct proportions rule of 3:-
if ab
c then
(b)inverse proportions rule of 3:-
if ab
c then
formula:- (i)direct method----
(ii)indirect or inverse proportions xy=k
GIVEN:- method used is called indirect or inverse proportions method
w1 =5,w2=,p1=20,p2=?,d1=8,d2=10
p2 =15
Question 15.
Answer:
theorem1:- The Rule of Three is a Mathematical Rule that allows you to solve problems based on proportions. By having three numbers: a, b, c,
(a)Direct proportions rule of 3:-
if ab
c then
(b)inverse proportions rule of 3:-
if ab
c then
formula:- (i)direct method----
(ii)indirect or inverse proportions xy=k
given:-w1=18,w2=?,p1=5,p2=10,d1=15,d2=10
method used is called indirect or inverse proportions method
w1 =24