RATIO AND PROPORTION

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