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Find the ratio at which rice at Rs.15.20 per kg is mixed with rice at Rs.18.10 per kg to get a mixture worth Rs.16.30 per kg.
Question

Find the ratio at which rice at Rs.15.20 per kg is mixed with rice at Rs.18.10 per kg to get a mixture worth Rs.16.30 per kg.

A.

15:13

B.

13:15

C.

11:18

D.

18:11

Correct option is D

Given:
​Price of first type of rice = Rs. 15.20/kg
Price of second type of rice = Rs. 18.10/kg
Price of the mixture = Rs. 16.30/kg

Formula Used:
Price per kg=Total CostTotal Weight\text{Price per kg} = \frac{\text{Total Cost}}{\text{Total Weight}}

Solution:
​Let's assume we mix x kg of rice at Rs. 15.20/kg with y kg of rice at Rs. 18.10/kg.
Cost of x kg of rice = 15.20x
Cost of y kg of rice = 18.10y

Total cost = 15.20x + 18.10y
Total weight = x + y

Price per kg=Total CostTotal Weight\text{Price per kg} = \frac{\text{Total Cost}}{\text{Total Weight}}
​​
16.30=15.20x+18.10yx+y16.30 = \frac{15.20x + 18.10y}{x + y}
​​16.30x+16.30y=15.20x+18.10y16.30x + 16.30y = 15.20x + 18.10y​​
1.10x=1.80y1.10x = 1.80y​​
xy=1.801.10xy=1811\frac{x}{y} = \frac{1.80}{1.10} \\\frac{x}{y} = \frac{18}{11}

​​Therefore, the ratio of the two types of rice is 18:11.

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