RATIO AND PROPOTION
RATIO: comparison of two things by means of
division .Let us understand
M/N
=M%N=M:N
Here M is compared to N (should know meaning of comparison), and these
comparison should be unique, it is not like multiply same number on numerator
and denominator.
PROPOTION: It is same like ratio but it is multiply same number on numerator and denominator.
.i.e. M/N=M*a/N*a
Or 1/3=4/12=12/36
Some Points to remember:
1) Find Which Ratio Is Smaller Or Greater Or Equal
Suppose two ratios M/N and Y/Z
is given
·
If given that M/N > Y/Z then relation should be M*Z > Y*N (don’t remember just make cross
multiplication you will get the relation).
OR vice versa if you calculate the relation M*Z > Y*N then you can easily find which ratio
is greater M/N > Y/Z .
·
If given that M/N < Y/Z then relation should be M*Z < Y*N (don’t remember just make cross
multiplication you will get the relation).
OR vice versa if you
calculate the relation M*Z <
Y*N then you can easily find which
ratio
is greater M/N < Y/Z .
·
If given that M/N = Y/Z then relation should be M*Z =
Y*N (don’t remember just make cross multiplication you will get the relation).
OR vice versa if you
calculate the relation M*Z =Y*N then you can easily find which ratio
·
is greater M/N = Y/Z
2) Middle Term And
Extremes :
Suppose the ratio M/N and Y/Z
M/N=Y/Z
Here M and Z is known as Middle Terms
Here N and Y is known as extremes Terms
IF M/N=Y/Z
Then Product of Middle
Terms = product of extremes Terms
3) Continued Proportion Or Mean Proportion:
If we have ration/proportion M/N and X/Y ,if middle terms are equal then
it is
Known as continued
proportion.
M/N=X/Y
M/N=N/Y [N=X]
M*Y=N2
.i.e. PRODUCT
OF EXTRESME = (MIDDLE TERM)2
4) Relation Among Ratio:
IF a: b and
b: c is given then find ratio
relation a: b: c
To solve such type of question trick is
make same the common terms in the ratio.
Then only find relation.
Example : if a:b=3:6 and b:c=4:2 then find a:b:c
Here common term is b thus
make equal them thus new ratio is
Now a :b=3:6 , b:c=4:2
a:b =3*4:6*4 , b:c=6*4:6*2
a:b =12:24,
b:c=24:12
Now
a:b:c=12:24:12
=1:2:1
END OF THEORY
QUESTION
QUESTION 1:
AN QUANTITY OF APPLE IS DIVIDED BETWEEN P,Q,R IN THE RATIO 2:5:7 RESPECTIVELY.
IF
TOTAL OF P AND R SHARE IS 800 MORE THAN Q SHARE .THEN FIND Q QUANTITY .
Solution: Given that P:Q:R=2:5:7
Letus suppose total apple is
A.
Use formula…
His quantity= (
his ratio * total quantity )/ total ratio
Now P quantity=2A/14
Q quantity=5A/14
R quantity=7A/14
According to question
(2A/14 )+ (7A/14)- ( 5A/14) =800
4A/14 =800
A=2800
NOW Q QUANTITY WILL BE
=5*2800/14
=1000
QUESTION 2:
A BAG CONTAINS 50P, 25P ,10P COINS IN THE RATIO 5:9:4 .amounting to ₹ 206.FIND
NUMBER OF COINS OF
EACH TYPE IN RUPEES.
Solution :
Let total no of coin is X,
Total no 50P coins in Paise = 5*X/14
Total no 50P coins in Rupees = 5*X/2*14
Total no 25P coins in Rupees = 9*X/4*14
Total no 25P coins in Rupees = 4*X/10*14
Now
(5*X)/(2*14) + ( 9*X)/(4*14) + ( 4*X)/(10*14) =206
(5X/28) + (9X/56)+
(4X/140)=206
X=40*14
Total no 50P coins in
Rupees = 5*X/2*14=5*20=100
Total no 25P coins in
Rupees = 9*X/4*14=9*20=180
Total no 25P coins in
Rupees = 4*X/10*14=4*20=100
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