85 kg of a mixture contains milk and water in the ratio 27:7. How much  more water is to be added to get a new mixture containing milk and  water in the ratio 3:1? Chapter/Topic:   Comparing quantities

# 85 kg of a mixture contains milk and water in the ratio 27:7. How much  more water is to be added to get a new mixture containing milk and  water in the ratio 3:1? Chapter/Topic:   Comparing quantities

1. A
5kg
2. B
6.5kg
3. C
7.25kg
4. D
8kg

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### Solution:

Total mixture= 85 kg,
let:  m = amount of milk
85 - m = amount of water.
Ratio = 27:7 (milk:water),
27/7m/(85-m)
27Solve for m using cross-multiplication:
27(85−m)=7m
2295−27m=7m
2295=34m
m=135/2
135/2 kg milk, which means that we have:
water=85 - 135/2
=170/2 - 135/2
=35/2 kg water
water to be added to make the ratio 3:1.
Let n = amount of water added.
3/1=(135/2)/(35/2+n)
Now, solve for n.

3(35/2+n)=135/2
105/2+3n=135/2
3n=30/2
n = 5
Hence, 5 kg water is to be added to get a new mixture containing milk and  water in the ratio 3:1.
Hence, Option (1) is the correct answer.

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