0 ratings0% found this document useful (0 votes) 44 views4 pages2
Copyright
© © All Rights Reserved
We take content rights seriously. If you suspect this is your content,
claim it here.
Available Formats
Download as PDF or read online on Scribd
Tey fw quello ae decay
satan a ong
{rato and proportion find their appt concepts
vsed on sped & distance near equa Pb,
‘pdmany more Althe concepts ang eet Pare
‘pRatioand Proportion are dlocuned nee ea
Sap through the rules carefaly, Assad
IMPORTANT Ponts
Ratio~The comparative relation betwean
uuantties of same type is called ratio, amounts
Then aftranountse ering
nine eee erate
pe
pushes os btn ia
apes 1 Hour Hoar eae
eee eee
Cooucts
fraction. It shows
ints in comparision
Ripon:
ete,
‘is y, then, the ratio
Inratio 1st number Le. is called “antecedent
ind number Le. Y's called “consequent sme am
Watb = Gd, then a and d are called extremes'and b
ind care called means,
+ Product of extremes = Product of means,
Le. ad = be
Directly Proportional: Ifx=ky, where kis a constant,
hen we say that xis directly proportional toy. Itis writen
wsxey.
ab
k
Inversely Proportional : If x = where k is @
constant, then we say that x is inversely proportional toy.
ts written as xe 2
y
Proportion : When two ratios are equal to each other,
‘hen they are called proportional as
ab = e:d, then, a, b, ¢ and d are in proportion.
or,
us
abi ed
Eg. 2:5 = 6: 15, then we write 2:5
RULE 1 : It does not change the ratio, when we multiply
> divide antecedent and consequent ofthe rato by a same
on-zero number as-
b
a
th
=
b
egarbe a ac:be=a:b
al of
RULE 2 : What should be added to
(numbers) so that these become proportional Fes
of ratio Is called its inverse.
wed
five?
Let x should be added
RULE 9 : Mixed ratio - Let xy and P:@ be two ratios.
‘then Px: Qy is called mixed ratio,
RULE 4 : Duplicate Ratio-The mixed ratio of two equal
atios is called the duplicate Ratio as
‘duplicate ratio of ab is ab?
RULE 5 : Subduplicate Ratio-The square root of @
‘certain ratios called its subduplicate.
‘The subduplicate ratio of atb = Ja:Vb
RULE 6 : Triplicate Ratio-The cube of a certain ratio
Is called tripticate ratio.
‘The triplicate ratio of a:b = a? :b*
RULE7 -Ratlo-The cube root ofa certain.
Tatiois called subtriplicate ratio as-
‘The Subtriplicate Ratio of a:b = Ya:¥b
RULE 8 : Inverse Ratio-The Reciprocal of quantities,
Reciprocal or inverse ratio of
Be
»
18
ab
RULE 9 : Invertendo-The proportion in which
Je cin ec
‘antecedent and consequent quantities change their places,
's called tnvertendo, as~
Invertendo of a:b
isdia= de
means 5
RULE 10: Alternendo-Ifa:b :c:d is a proportion then,
ord
a
i 2
ie means.
A
@ scanned with OKEN Scanner Compmento ant dividenton!! there is 2
C6 then is components art tereciin $s
ath cod
{8+ bila bjste + aie do Seog
To simplify the propartion any one meshes of
ompersntn dtdendn tian wet Dison
directly be used. eine
RULE 14: Mean Proportion - Lt x be the mean
Proportion between a and b, then axxcrb (Peal constr)
ae
B= eee
x= feb
So, mean proportion ofa and b= Jab
Ix be the mean proportion between (xa) and tx-b)
then what will be the value of x7
asb
RULE 15 : Third proportional-Lct x be the third
proportional ofa and b then, |
box (Real condition) |
»
2 mer |
x
pute 372 cin!
Sais 0 A ON,
£2 aah
ace
a
ae
un 18 UAB ary A BE = 7A Me
gree
WABCO
sone ws ol:
ABay
RULE 10: 1fAB=xy. C= pq and CD = men the
QADempoi ye
(9) ABCD = epypyd * BYP = PRPS
CD = wary and DE = mothe
RULE 21: [fen amount R is to be divided berwenss
and Bin the ratio mn then
O) Pant of A=
aR
(9 Pan of B= Gon
(iu) Difference of part of A and B
where m>n
RULE 22 ; If the ratio of A and B is mn and de
| difference in their share is“R' units then,
«= Third proportional of a and
RULE 16 : Fourth Proportional- Let xbe the fourth |
proportional of a, b and c, then a:bi:e:x (Real condition)
©
apps mrbe
ole
|
|
be |
be
<. Fourth proportional of a. band ¢= — |
@ Pan of
of B= *R
PanofB= aoa
ul) The sum of parts of A and B= D2aR
mn
where m > n
RULE 23: Ifthe ratio of A and B is m:n and the part
Ais’R. then
W Share of B= xR
Gea —___
@ scanned with OKEN Scanner a
eee
(W Total share of A and 5. a
7
Um) Pillrence $9 shave of 4 gig %
Ben
where m>n om 7k
RULE24: Ifthe amount Ris
sn the ratio L:m:n, then Met among Bang
L
Whe share of A= FR
(The share of B =~
teman*®
(ii) The share of ¢ = 8
iyman*®
Difference in share of A ang p_ t=
m
temenR
where I> m
&
(0) Diference in share of = hy
eanic Umin R
‘where mon
Tea et #80064, Band C8 i: anand tne
utof Ais ‘R' then, cae
(0 Part of
(W Part of
m-n
(ti) Difference in parts of B and C =
xR,
(where m > n)
(+m ny
WI Total share of Band C= “*5* ALR
RULE 26 : If an amount is to be divided among A, B
@ Cin the ratio 1: m:n and the difference between A
Bis 'R, then
0 Part of ¢ =
xR, where 1> m.
Em
lemen
=m
xR
tt) Total share of A. B and C =
*ATIO AND pRopoRTION a eames:
MED yR, where
(u Diterence in share of Band C= am
I> mand m>n
RULE 27 : If there are notes of es
‘and 2’ rapees in a box in the ratio m:n
of notes is R’, then,
pecs, rupees
the total value
xR
(Number of notes of x rupees = Gant yn 24]
uw xR
(Number of notes of y rupees = [myn +28)
UW Number of notes of 2 rupees = Taameyn-ran) x
RULE 28 : adding/subtracting a certain quantity
‘®¥es new ratio, then multiplier
_~ [otal Quantity +Changein Quantity)
- ‘Sumof Ratios
= Then quantity
then the
water in third glass which contains aligation
ofboth glasses is
rae 38a) (ata)
RULE 0: Ifthe ratio of milkanid waterin the,
ofA litres pq then water must be added
of milk and water would be ris te
alligation
{nit so that ratio
Required amount of wate
RULE 91 : The ratio oftncome of two persons A and B
1s pq. If the ratio of their
‘monthly income of A and B,
°R rupees wil be
Monthly income of
RULE 92 : Let be a number which is subtracted
from a,b, cand d to make them proportional, then
ad-be
where [> m.
@d-(b+0
—_W 2).
@ scanned with OKEN Scanner —_{__ Lh
$$ arto ann proportion
SN
‘are im the ratio at ang
Let x'be
mrake them property NC Is ad two urnbers ‘1
Proportion Added toa.b,cand dto | RULE 94+ the ratlo becomes
fom sect ier i nereased 1 4
xe mon xale-)— Xle-g)
fsa-tbee) umber wi be adobe
Here,
order,
be
© and d should always be in ascending
then each rao
‘Then the to
pers aren the ratio aban,
RULE 36 : Two num 5 |
sgubtracted from each HUMPCE the ratio becomes etn,
xa(d-o) _, X0d-0)
warbe 2M “ad-be
two numbers will be = “ad-be
PROBLEMS BASED ON AGES
Importance : You would be knowing that such
questions are asked in different competitive exams.
Scope of questions : In these questions age/ratio of
ages of person /his relatives is asked for present /future
or past ages.
‘Way to success : Given rules and mental mapping in
these questions will save your time and labour.
Rule 1.
Ifthe ratio of present age and the ratio of age after
‘years is given then present age factor is given
by
(Difference in 2nd ratio) xtume
X= Difference in eross products of ratio)
Rule 2.
Ifx is the present age factor, and the difference in
cross product of ratio is zero then,
ume
X* [Dilference of ratio)
Rule 3.
Ifthe ratio of'some years ago’ and ‘after some years’
{s given, And Before t’ years, the ratio of ages of A
and B was a:b.
Present age of A= ax +t,
Present age of B = bx +t,
after ‘ts years, the ratlo of their ages will be
c:d.
(Diference In 2nd ratio) x (y +t
+: X= DDilference in cross products of the ratio)
When, the difference in ratios 1s equal, then
(yt)
X= (Difference in ratio)
Rule 4.
ifthe product of
[Product of ages of tO PEFSOnS
Product of ratio
resent ages is given, thea,
xe
Rule 5.
ifsum of present age and ratio of the ages ee
then, present age factor.
‘Sum of Present ages
‘Sum of ratio
Rule 6.
If thie rato of ages and difference in ages is ge
then,
difference between aj
difference in ratio
Rule 7. ’
“The ratio of ages of A and B was x: y"n'yearsa
xen
( Ifthe present age ratio is a:b. then. yb
(W) If after “m’ years, the ratio of ages wil ®
xen+m_p
:qthen,
peqthen venem q
Rule 8.
Ifa’ years before, the ratlo of ages of A.B aaf¢
was x;y :2, then the ratio of their present 4°?
(+m): y+): (+n)
Rule 9,
after m years, the ratio of ages of A and Bw ®
xy, then the ratlo of their present as"
(=m): (ym).
oot
@ scanned with OKEN Scanner
