Quality A and B rice, valued at Rs 35 per kg and Rs 65 per kg respectively, are mixed. The new average price of the mixture obtained is Rs 50 per kg. What is the ratio of the quantity of A and B in the mixture?
A. 1 : 2
B. 1 : 3
C. 1 : 1
D. 1 : 5
- AOption (a)
D
- BOption (b)
B
- COption (c)
C
- DOption (d)
A
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Correct answer
C
Why this answer is correct
Given:
The cost price of A = Rs 35 per kg
Cost price of B = Rs 65 per kg
The average price of the mixture = 50 per kg
Calculation:
Let the total quantity of rice be X kg.
Total cost price = 50 × X = 50X
Let the quantity of rice of variety A = A kg
Then, the quantity of rice of variety B = (X - A) kg
Total cost price of variety A = 35 × A = 35A
Total cost price of variety B = 65 × (X - A) kg
65(X - A) + 35A = 50X
15X = 30A
Or, X/A = 2/1
The ratio of variety A to variety B = A/(X - A) = 1/(2 - 1)
Ratio of A to B = 1 ∶ 1
∴ The required ratio is 1 ∶ 1.
Shortcut Trick
By using the allegation method
∴The ratio of variety A to variety B is 1 : 1