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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.

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.

Grade:12

5 Answers

Arun
25750 Points
6 years ago
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)
Meet
137 Points
6 years ago
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.
Meet
137 Points
6 years ago
Ghere is mistake in answer of arun ...................................................................................................,,,,,,,,,,,,
Rewa
20 Points
6 years ago
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!
Rewa
20 Points
6 years ago
(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

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