Math, asked by pascaL1, 1 year ago

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

pascaL1: give me the answer

Answers

Answered by yasummu

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.

rishiv: i think it is incorrect :)

yasummu: it is absolutely right. what made you thunk so?

rishiv: coz ur and her answer is different na that's y

rishiv: mera answer bhi 3/2 hi nikla hai 13/21 nhi nikla !!

yasummu: hame pehla waala number find karna hai. aur use find karne ke liye addition or subtraction relation diya hai.

yasummu: 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.

rishiv: 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???

yasummu: for eg: If the numerator is 1 then the denominator is 1 + 8

rishiv: 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

Answered by pahiroy1221

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 ..........................^_^

yasummu: No you have to find the initial rational number on which by some operations we 3/2. So the ans is 13/21.

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