# The numerator of rational number is less than the denominator by 8. if denominator is decreased by 1 and numerator is increased by 17 then the number obtained is 3/2. find the rational number

2
by pascaL1

2015-11-17T06:53:53+05:30

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Let the numerator be  `x`
Then the denominator = `x+8`
And the fraction will be x/x+8
Numerator increased by 17, and denominator decreased by 1 we get the fraction as
(x+17)/(x+8-1)
But the fraction is given as 3/2
⇒ (x+17)/(x+7) = 3/2
⇒3(x+7) = 2(x+17)
⇒3x+21 = 2x+34
⇒3x-2x = 34-21
⇒x = 13
∴Numerator = x = 13
Denominator = x+8 = 21
Therefore the fraction is  13/21.
hame pehla waala number find karna hai. aur use find karne ke liye addition or subtraction relation diya hai.
aur to aur 3/2 agar answer hai to numerator denominator se 8 kum rehna chahiye. but it is not. Isiliye 3/2 is not the correct answer answer. if you want the explanation i am ready to give.
The numerator of rational number is less than the denominator by 8.if it is given then numerator will be less then that of the denominator right???
for eg: If the numerator is 1 then the denominator is 1 + 8
but in the question it is written thatThe numerator of rational number is less than the denominator by 8.means that the numerator is less then the denominator by the factor 8
2015-11-17T11:30:27+05:30
according to the given data ,
let the denominator = x
and then the numerator is less than the denominator by 8
therefore the numerator = x - 8
now A.T.Q ,
x - 8 + 17 / x -1 = 3/2
x + 9 / x - 1 = 3/2
by cross multiplication ,
2 (x + 9 ) = 3 ( x - 1 )
2x +18 = 3x - 3
2x - 3x = - 3 - 18
- 1x = - 21
x = 21
therefore the value of x = 21
now ,
x - 8 + 17 / x - 1 ( A.T .Q )
= 21 - 8 +17 / 21 - 1
= 30 / 20
= 3 / 2
therefore the rational number = 3 / 2
i hope that this will help u ..........................^_^
No you have to find the initial rational number on which by some operations we 3/2. So  the ans is 13/21.