Friday, 13 March 2015

RATIO AND PROPORTION




The ratio is Denoted as X:Y

X:Y=X/Y

Eg:

Value=40
That in the Ratio 5:3
then the 5 part of 40=?
               3 part of 40=?
40/(5+3)=40/8=5
One part value=5
Then 5 part=5*5=25
         3 part=5*3=15
25+15=40

QUESTION AND ANSWER


If the position of the digits of a two digit number are interchanged,the number newly formed is smaller then the original number by 45.Also the ratio between new number and the original number is 3:8 respectively.what is the original number?

The two digit number=XY
Interchanged number=YX
YX is smaller then original by 45==>XY=YX+45-----(1)
YX:XY=3:8-------(2)
XY-YX=45------By (1)
3~8=YX~XY
5=45
one part=8 so
YX= 3 part=3*8=27----------By(2)
XY= Interchage of digits=72
Original number=72

(OR)

10X + Y=10Y+X+45
9X-9Y=45
X-Y=5--------(1)
(10Y+X)/(10X+Y)=(3/8)
30X+3Y=80Y+8X
22X-77Y=0--------(2)
Solve (1) and (2)
55Y=110
Y=2
X=7
Original number=72

The digits of a two digit number are in the ratio of 2:3 and the number obtained by interchanging the digits is bigger then the original number by 27 what is the original number ?

XY=>X:Y=>2:3
YX-XY=27
Here individual digit ratio is given so try to trace from options 
1)63
2)48
3)96
4)69
we know they are in 2:3 ratio so 96 eliminated
yx-xy=27
36-63= not possible
84-48=(2+30+4)=36 Wrong
96-69=(1+26)=27 Right Answer

(OR)



Eg:
------------
56=50+6
(10*X)+6
X=5
------------

We knew the two digit number is always 10 th unit+some X

So 10X-Y---->Original number
X:Y=2:3 
(10Y+X)-(10X+Y)=27----->(1)
9Y-9X=27
Y-X=3
Y=X+3--------->Put in(1)
X/(X+3)=(2/3)
X=6
Y=9
Original number=69

Ages of A and B in the ratio 2:3 Respectively,
Six year hence the ratio of their ages will become 8:11 Respectively,
What is B's Present age ?

A/B=2/3
Six years Hence(After)
A/B=8:11

Now2X/3X
After 6 Years (2X+6)/(3X+6)=8/11
cross multiply them
11(2X+6)  = 8(3X+6)
22X+66  = 24X+48
22X-24X=48-66
2X=18
X=9
Now=>18:27
A=18
B=27








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