excelingmat wrote:
Half of the volume of the milk and water mixture of ratio 7:5 is converted into a mixture of ratio 3:1 by the substitution(or replacement method) the mixture of ratio 7:5 was formed from the mixture 7:3 by adding the water in it. if 240 L milk is required in the replacement method ,what it the total amount of water was added t6o prepare the mixture 7:5 ?
a) 100 L
b) 50 L
c) 400 L
d) 300 L
e) 200 L
Source - NCERT
Hi,
ofcourse, this Q is not a typical GMAT Q and also not properly replicated from source..
but still lets solve it..
2 actions have been done on the mix...
1)7:3 is converted into 7:5 mix..
2) half of the mix of 7:5 is converted in 3:1 by adding 240l milk..
lets start with 2 action as more info is given there..let the mix common ratio be 2x..
so total sol = milk:water=7*2x:5*2x
240 l milk is added to half of it to make it 3:1..
so (7x+240)/5x =3:1..
we get x=30 or 2x=60..
so the sol is 7*60:5*60=420:300..
now we look at the first action ..this was created from 7:3 mix...
so say x was added to get this ratio...
so 420/(300-x)=7/3..
here x =120..
but 120 does not seem to be a choice..
now why 120 has to be correct..
initial milk:water=420:180=7:3(this is given to us)..
120 l of water is added= 420:180+120=420:300=7:5(again this confirms with what has been given)
240 l of milk is removed from half the mixture..
half the mix=210:150..
add 240 l milk...
210+240:150=450:150=3:1(satisfies the given data in Q)..