SOLUTION: 40 kg of broken rice at the rate of Rs. 5 per kg less than the fine quality rice is mixed into 100 kg rice of fine quality. The price of the mixture is Rs.12 per kg. Find the per k

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Question 1011280: 40 kg of broken rice at the rate of Rs. 5 per kg less than the fine quality rice is mixed into 100 kg rice of fine quality. The price of the mixture is Rs.12 per kg. Find the per kg price of the fine qulaity of rice.
Found 3 solutions by josgarithmetic, addingup, MathTherapy:
Answer by josgarithmetic(39617) About Me  (Show Source):
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                    PRICES
Broken              R-5 Rs. Per Kilogram
Fine Quality        R  Rs. Per Kilogram

The mixture of the broken type and the fine quality type is Rs. 12 per kilogram.
40 kg of the broken, 100 kg of the fine.

highlight_green%28%2840%2A%28R-5%29%2B100%2AR%29%2F%2840%2B100%29=12%29------this is the important part. The rest is just arithmetic.

highlight%28R=13%263%2F7%29


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MORE DETAILS
Price is the ratio of the money to the mass.
R        the price Rs. per kilogram for the fine quality rice.
R-5      the price in Rs. per kilogram for the broken type rice.

Cost for the broken type is 40%2A%28R-5%29
Cost for the fine quality type is 100%2AR
Cost for both those quantities of rices is  40%28R-5%29%2B100R, units of Rs.

The mass in kilograms for the mixture of rices is given, 40%2B100=140%2Akilograms.


The needed price for the mixture must be 12 Rs. per kilogram.

MONEY%2FMASS=12

highlight%28highlight_green%28%2840%28R-5%29%2B100R%29%2F140=12%29%29


Answer by addingup(3677) About Me  (Show Source):
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So we have a total of 40+100= 140kg of rice at Rs 12 per kg
And we know that the 40 kg of broken rice are Rs 5 per kg
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140(12)-40(5)= 100(x)
1680-200= 100x
1480= 100x
14.80= x or more elegantly:
x= 14.80
The price of the fine quality is Rs 14.80 per kg.
J

Answer by MathTherapy(10552) About Me  (Show Source):
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40 kg of broken rice at the rate of Rs. 5 per kg less than the fine quality rice is mixed into 100 kg rice of fine quality. The price of the mixture is Rs.12 per kg. Find the per kg price of the fine qulaity of rice.
Let per-kg price of fine rice be F

Then we get: 5(40) + F(100) = 12(40 + 100)

Solve for F to get: highlight_green%28%22%24%2214.80%29 per kg