Question : In what ratio sugar of Rs. 30 per kg should be mixed with sugar of Rs. 40 per kg so that the mixture is worth Rs. 37 per kg?
Option 1: 8 : 9
Option 2: 3 : 7
Option 3: 4 : 3
Option 4: 9 : 5
Correct Answer: 3 : 7
Solution :
Let's assume that the ratio in which the two types of sugar are mixed is $x:y$
The cost of sugar of Rs. 30 per kg is 30$x$
The cost of sugar of Rs. 40 per kg is 40$y$
The mixture is worth Rs. 37 per kg
So, the cost of the mixture is $37(x+y)$
⇒ $30x + 40y = 37(x+y)$
⇒ $40y − 37y = 37x − 30x$
⇒ $3y = 7x$
⇒ $y$ : $x$ = 3 : 7
Hence, the correct answer is 3 : 7.
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