The denominator of a rational number is 7 more than the numerator. If 1 is added to the numerator and 1 is subtracted form denominator the new number is 1/2.Find the rational number.
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ATQ,
The denominator of a rational number is 7 more than the numerator
=> x/x+7 --equation 1
If 1 is added to the numerator and 1 is subtracted form denominator the new number is 1/2
=>x+1/x+6=1/2
=>2x+2=x-6
=>2x=x-8
=>x=-8/2
so x=-4
Putting this value in equation 1
=>-4/-4+7
REQUIRED RATIONAL NUMBER => -4/3
The denominator of a rational number is 7 more than the numerator
=> x/x+7 --equation 1
If 1 is added to the numerator and 1 is subtracted form denominator the new number is 1/2
=>x+1/x+6=1/2
=>2x+2=x-6
=>2x=x-8
=>x=-8/2
so x=-4
Putting this value in equation 1
=>-4/-4+7
REQUIRED RATIONAL NUMBER => -4/3
But in book answer is 4/11
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Let the numerator be x and the denominator be y . Then according to question, x + 7 = y ....... (1) . If 1 is added to the numerator and 1 is substracted from denominator the new no. is 1/2. Therefore, ( x+1 ) / ( y-1 ) = 1/2. By cross multiplication we get 2x + 2 = y - 1 which is equal to 2x - y = -3 .......(2). Now adding both the equations we get x = 4. From equation (1) we know x+ 7 = y . Putting the value of x=4 we get y = 4+7 which is equal to 11. Hence the ration no. will be x/y = 4/11.
Your book's answer is wrong
No the book answer is correct
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