Three different coffee blends are formed using the 4 varieties A,B,C and D. The first blend has A and B in the ratio 2:3, second blend has A and C in 2:5 and third has A and D in 2:7. if the first second and third blends are taken in the ratio 3:4:5 to form a new blend, find the ratio of quantity of A to the quantity of other 3 varieties in the new blend.
A)0.404
b)0.532
c)0.643
d)0.678

I actually got 0.4041... exactly :))

Just check again, must be some minor calculation error

Thanks! I am getting the answer as 0.454, is that what you got? option 1 seems to be the closest!

Answer is option 1?

Assuming volume of 5x7x9 (LCM from the different coffee blends ratio) of every coffee blend we get the following quantities-

Mix 1- A=2/5x5x7x9=126, B=3/5x5x7x9=189
Mix 2 A=2/7X5X7X9=90, C=5/7X5X7X9=225
Mix 3 A= 70 , D=245 (in a similar way)

Required ratio= (3/12x126+4/12x90+5/12x70)/(3/12x189+4/12x225+5/12x245)=0.404