Question : In what ratio must a grocer mix two varieties of sweets costing Rs. 30 and Rs. 20 per kg respectively to get a mixture worth Rs. 25 per kg?
Option 1: $2:3$
Option 2: $1:1$
Option 3: $5:4$
Option 4: $4:5$
Correct Answer: $1:1$
Solution :
Let the two varieties of sweets costing Rs. 30 and Rs. 20 per kg be mixed in the ratio of $x:y$ respectively.
Weighted Average=$\frac{\text{Quantity of first variety×Price per kg of first variety)+(Quantity of second variety×Price per kg of second variety)}}{\text{Total quantity}}$
⇒ 25 = $\frac{(30x+20y)}{x+y}$
⇒ 25($x+y$) = 30$x$+20$y$
⇒ 25$x$ + 25$y$ = 30$x$ + 20$y$
⇒ 5$y$ = 5$x$
⇒ $x:y$ = 1 : 1
Hence, the correct answer is $1:1$.
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