Question

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 ?

• A. 5 kg
• B. 6.5 kg
• C. 7.25 kg
• D. 8 kg

Answer 1

Answer: (A)

5 kg

total mixture= 85 kg,
let: m = amount of milk
85 - m = amount of water.
ratio = 27:7 (milk:water),
$\frac{27}{7}=\frac{m}{(85-m)}$
Solve 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.
$3/1=\left(135/2\right)/(35/2+n)$
Now, solve for n. Again, start with cross multiplication:
$3(35/2+n)=135/2$
$105/2+3n=135/2$
$3n=30/2$
$n=5$
Answer (A) 5