pea302_lec#9_ratio & proportion.pps

8/9/2019 PEA302_Lec#9_Ratio & Proportion.pps

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PEA302 –

Lecture #9RATIO ANDPROPORTION

PreparedBy:

Mr. V !"aPEA302 A'a yt ca &) !*II :: V !"a A"u$a


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Ratio

PEA302 A'a yt ca &) !*II :: V !"a A"u$a


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Fourth Proportional:

If a : b = c : d , then d is called the fourth proportionalto a, b, c .

Third Proportional:

a : b = c : d , then c is called the third proportion to a and b .

Mean Proportional:

!ean proportional "etween a and b is # ab .



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$uplicate Ratio



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%uestion %&.'

Two num"ers are respecti ely )*+ and*+ more than a third num"er. The

ratio of the two num"ers is:-. ) :

. / :

0. 1 : $. 2 : 3



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A'!+er: 4ption ,E-p a'at ':5et the third num"er "e x .

Then, 6rst num"er = ')*+ of x = ')* x/100 = 2 x/ 7econd num"er = ' *+ of x = ' * x/100 =

/ x/ )Ratio of 6rst two num"ers = 2 x/5 : / x/2 = 1 :

.



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%uestion %&.)

The sum of three num"ers is &8. If theratio "etween the 6rst and secondnum"er is ) : / and the ratio "etweensecond and third num"er is : 8, 6ndthe second num"er.-. )*

. /*0. 18

$. 9one of thesePEA302 A'a yt ca &) !*II :: V !"a A"u$a


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%uestion %&./

- sum of money is to "e distri"utedamon -, , 0, $ in the proportion of : ) : 1 : /. If 0 ets Rs. '*** more than$, what is ;s share<-. Rs. **

. Rs. ' **0. Rs. )***$. 9one of these



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A'!+er: 4ption ,E-p a'at ':

5et the shares of -, , 0 and $ "e Rs. x , Rs. ) x , Rs. 1 x and Rs. / x respecti ely.

Then, 1 x / x = '*** x = '***.;s share = Rs. ) x = Rs. () x '*** =

Rs. )***.PEA302 A'a yt ca &) !*II :: V !"a A"u$a


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%uestion %&.1

7eats for !athematics, Physics andiolo y in a school are in the ratio : 3

: 8. There is a proposal to increasethese seats "y 1*+, *+ and 3 +respecti ely. >hat will "e the ratio ofincreased seats<

-. ) : / : 1. 2 : 3 : 8

0. 2 : 8 : &$. 9one of thesePEA302 A'a yt ca &) !*II :: V !"a A"u$a


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A'!+er: 4ption AE-p a'at ':4ri inally, let the num"er of seats for !athematics,

Physics and iolo y "e x , 3 x and 8 x respecti ely.9um"er of increased seats are ('1*+ of x , (' *+of 3 x and ('3 + of 8 x .'1*?'** x x , ' *?'** x 3 x and '3 ?'** x 8 x

3 x , )' x/2 and '1 x . The required ratio = 3 x : )' x/2 : '1 x '1 x : )' x : )8 x ) : / : 1.



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%uestion %&.

If 1*+ of a num"er is equal to twothird of another num"er, what is theratio of 6rst num"er to the secondnum"er<-. ) :

. / : 30. : /$. 3 : /



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A'!+er: 4ption ,E-p a'at ':

5et 1*+ of - = )?/ Then, 1*?'** - = )?/ )? - = )?/

-? = )?/ x ?) = ?/- : = : /.



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%uestion P&.'

Two num"er are in the ratio / : . If & issu"tracted from each, the newnum"ers are in the ratio ') : )/. Thesmaller num"er is:-. )3

. //0. 1&$.



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%uestion P&.)

In a "a , there are coins of ) p, '* pand p in the ratio of ' : ) : /. If thereis Rs. /* in all, how many p coins arethere<-. *

. '**0. ' *$. )**



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A'!+er: 4ption ,E-p a'at ':5et the num"er of ) p, '* p and p coins "e

x , ) x , / x respecti ely. Then, sum of their alues= Rs. ) x/100 A '* x ) x/100 A x / x/100 =Rs./*

2* x/100 = /* x = *.Hence, the num"er of p coins = (/ x * =

' *.PEA302 A'a yt ca &) !*II :: V !"a A"u$a


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pea302_lec#9_ratio & proportion.pps

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