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Grade: 12

                        

If 1/3 be added to the numerator of a certain fraction, the fraction is increased by 1/15 and if ¼ be taken from the denominator the fraction becomes 8/19 find the fraction.

2 years ago

Answers : (5)

Arun
24742 Points
							
Dear student
 
Let the fraction is x/y
Now
[x+(1/3)]/y = x/y + 1/15
(3x +1)/3y = (15 x + y)/15
45x +15 = 45 xy + 3y²
 
x/(y-1/4) = 8/19
4x/(4y-1) = 8/19
76 x = 32y -8
19x = 8y -2
 
Now you can solve it
 
Regards
Arun (askIITians forum expert)
2 years ago
Meet
137 Points
							There is mistake in above in first it as [x+1/3]/y= x/y + 1/15 and it can be further simplified as y=5 and the other equation is x/(y-0.25)=8/19 then by this  equation we get 38=19x then x=2 so therefore 2/5 is the fraction.
						
2 years ago
Meet
137 Points
							Ghere is mistake in answer of arun ...................................................................................................,,,,,,,,,,,,
						
2 years ago
Rewa
20 Points
							It can be solved by more simpler way....(X+1/3)= X+ 1    Y         Y  15   ..    .  X +(1/3) = X + 1        Y      Y        Y   15   ..    .  (1/3) = 1           Y    15 Gives 15/3 = Y  Thus,   Y= 5      X       =  8(Y-1/4)       19 ........ CONDITION ÍÍ       Substituting value of Y in equation,we get,         X.    = 8     -------   -------  (5-1/4).  19=.   X.    =.  8    -------    -----   19/4.      19= 4X.     =. 8--------       ----  19.         19   ..    .   4X = 8           X = 2 The required fraction = X = 2                                         -----  ---                                           Y.    5Tally IT!
						
2 years ago
Rewa
20 Points
							(X+1/3 )/ Y = X/Y + 1/15....X/Y + (1/3)/Y = X/Y + 1/15 (splitting terms)..(1/3)/Y = 1/15(elimination of common trm)Y=15/3 = 5 ........X/(Y-1/4) = 8/19.....X/(5-1/4) = 8/19....(substituting Y)X/(19/4) = 8/19....X= 2Required fraction= 2/5
						
2 years ago
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