Theorem:
A person has a liquid of Rs x per litre. The ratio
in which water should be mixed in that liquid, so that after
selling litre mixture at Rs y per litre he may get a profit of P%, is given by
=
(
y
)
(x - y)
+
(
p
)
x
100
Example :
A person has a chemical of Rs 25 per litre. In what
ratio should water be mixed in that chemical so that
after selling the mixture at Rs 20/litre he may get a
profit of 25%.
Detail Method :
Let the ratio of chemical to water in
the mixture be a : b.
Cost price of the chemical is Rs 25 per litre
∴ cost price of a litre of the chemical = Rs 25
Assume that the cost price of water be Rs 0 per litre
Now, according to the question,
Selling price of the mixture = Rs 20 per litre
∴ Selling price of (a + b) litres of the mixture
= Rs (a + b) 20
Cost price of (a + b) litres of the mixture
= (a + b) X 20 X
100
125
(By the rule of fraction)
= Rs (a + b) 16
or,25 X a + 0 X b = (a + b) 16
or, 9a = 16b
or,
a
=
16
b
9
So a : b = 16 : 9
So Required ratio = 16 : 9.
Ailigation Method :
In this question the alligation
method is applicable on prices, so we should get the
average price of mixture.
SP of mixture = Rs 20/litre, profit = 25%
∴ average price = 20 X
100
= Rs 16/litre
125
Chemical
Water
25
16
0
16
9
∴ Chemical : Water = 16 : 9
Quicker Method : Here you can use direct formula :
reqd ratio =
(
20
)
(25 - 20)
+
(
25
)
X 25
100
=
80
=
16
= 16 : 9.
45
9
Exercise :
A milk seller pays Rs 500 per kilolitre for his milk. He
adds water to it and sells the mixture at 56 P a litre, thereby
making altogether 40% profit. Find the proportion of
water to milk which his customers receive.
A person has a chemical of Rs 50 per litre. In what ratio
should water be mixed in that chemical so that after selling
the mixture at Rs 40 per litre he may get a profit of
50%.
A man buys milk at Rs 5 a litre and mixes it with water. By
selling the mixture at Rs 4 a litre he gains 12 1/2 per cent
on his outlay. How much water did each litre of the mixture
contain?