What quantity of rice at rs.10 per kg should be mixed with 48 kg of rice at rs.6 per kg and 30 kg of rice at rs.8 per kg such that a profit of 25% is earned on selling the mixture at rs.10 per kg?
Answers
Solution:
Step 1:
As the trader makes 25% profit by selling the mixture at Rs.40/kg, his cost per kg of the mixture = Rs.32/kg.
Step 2:
C.P of 1 kg of rice of 1st kind = Rs. 42
C.P of 1 kg of rice of 2nd kind = Rs. 24
Mean price = Rs. 40
By the rule of alligation, we have:
C.P. of 1kg of C.P. of 1kg of
rice of 1st rice of 2nd
kind (Rs. 42) kind (Rs. 24)
\ /
Mean Price
(Rs. 32)
/ \
40 - 24 : 42 - 32
(8) (10)
Let the amount of Basmati rice being mixed be x kgs.
8:10=x:25 ⇒ (
4
5
)=(
x
25
) ⇒ x=20 kgs.
Alternatively:
Let the amount of Basmati rice being mixed be x kgs.
As the trader makes 25% profit by selling the mixture at Rs.40/kg, his cost per kg of the mixture = Rs.32/kg.
i.e. (x×42)+(25×24)=32(x+25)
⇒ 42x+600=32x+800
⇒ 10x=200 ⇒ x=20 kgs
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