A fraction becomes 10/7 if 2 is added to both numerator and denominator. If however 3 is subtracted from both numerator and denominator, the fraction becomes 5/2. What is the fraction?
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according to question;
x+2/y+2=10/7 ......(1)
x-3/y-3=5/2 ......(2)
(where numerator = x ; denomerator = y)
From equation (1) we get
(x+2)7 = 10( y+2)
7x + 14 = 10y + 20
7x - 10y =20 - 14
7x - 10y = 6 ............(3)
similarly;
from equation (2) we get
5y - 2x = 9 .............(4)
from (3) we get
x = 6+10y/7 ............(5)
substitute x = 6+10y/7 in (4) we get
5y - 2( 6+10y/7)=9
5y -(12+20y/7) = 9
35y-12 - 20y/7 =9
15y- 12 =9×7
15y = 75
y= 5 ....... (6)
now substitute y =5 in (5) equation we get
x = 6+10(5)/7
x=6+50/7
x=56/7
x= 8 ........ (7)
Hence fraction is 8/5
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