If the numerator of a fraction is increased by 2 and denominator by 1 it becomes 5/8 and if the numerator and the denominator of the same fraction and each increased by 1 , then fraction becomes equal to 1/2. Find the fraction.
If the numerator of a fraction is increased by 2 and denominator by 1 it becomes 5/8 and if the numerator and the denominator of the same fraction and each increased by 1 , then fraction becomes equal to 1/2. Find the fraction.
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Let the numerator be x
denominator be y
According to first condition
x+2/y+1 =5/8
8x+16=5y+5
8x-5y+11=0
8x-5y=-11 eq_1
According to the second condition
x+1/y+1=1/2
2x+2=y+1
2x-y+1=0
2x-y= -1 eq_2
Solve in equation 1
8x=5y-11
x=5y-11/8 eq_3
put in equation 2
2(5y-11/8)-y =-1
10y-22/8-y=-1
taking LCM. LCM is 8
10y-22-8y=-1
2y=22-1
2y=21
y=21/2
y=1.5
put in equation 3
x=5(1.5)-11/8
x=7.5-11/8
x=0.4375