Let weight of tea worth .75 $ = w1
and weight of tea worth .93 $ = w2
w1 + w2 = 10 --- equation 1
.85 = ( w1*.75 + w2* .93 )/(w1+ w2 )
=> .85 w1 + .85 w2 = .75 w1 + .93 w2
=> .10 w1 -.08 w2 = 0
=> 10 w1 - 8 w2 = 0 --- equation 2
From 1 ,
8 w1 + 8 w2 = 80 --- equation 3
From equations 2 and 3 , we get
18 w1 = 80
=> w1 = 40/9
and w2 = 50/9
Answer D , which is in mixed fraction.
Alternatively , we can use scale method
.75 -----.85 ---- .93
.85 is at a distance of .1 from .75 and .08 from .93
The distances of .85 from .75 and 93 are in ratio of 10 : 8 , that is 5:4
Therefore , the weights will be in inverse proporation 4:5
Therefore , w2 = 5/(4+5) * 10 = 50/9
Alternatively, We can also use estimation here and eliminate options A, B and C as the weight of .93 $ variant
has to be more than 50% of 10 pound , i.e 5 pounds . If w1=w2 , then resultant mix would have been of .84 $.
We can also eliminate option E because then the resultant mix will be very close to .93 , only marginally less .
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