How many kg of rice at Rs 54 per kg must be mixed with 30 kg of rice at Rs 40 per kg, so that on selling the mixture at Rs 48.4 per kg, there will be a profit of 10%?

Let the quantity of rice mixed at Rs 54 per kg be x kg.
Find the Cost Price (CP) of the mixture:
Selling Price (SP) of the mixture = Rs 48.4 per kg
Profit = 10%

CP of mixture=
1+
100
Profit%
​

SP
​
=
1.1
48.4
​
=Rs 44 per kg
Using the rule of Alligation:

Cost of type 1 rice (C
1
​
) = Rs 54

Cost of type 2 rice (C
2
​
) = Rs 40

Mean price (M) = Rs 44

Quantity of type 2
Quantity of type 1
​
=
C
1
​
−M
M−C
2
​

​
=
54−44
44−40
​
=
10
4
​
=
5
2
​

Given that the quantity of type 2 rice is 30 kg:

30
x
​
=
5
2
​

x=
5
2
​
×30=12 kg