In what ratio must tea at Tk 62 per kg be mixed with at Tk 72 per kg so that the mixture must be worth Tk 64.5 per kg?

Question: In what ratio must tea at Tk 62 per kg be mixed with at Tk 72 per kg so that the mixture must be worth Tk 64.5 per kg?

Solution:
Let the quantity of the tea that is Tk 62 per kg be x kg and that of tea that is Tk 72 per kg be y kg.

Hence, the required ratio is x : y

Price of x kg tea = Tk 62x
Price of y kg tea = Tk 72y

If we mix both varieties of tea, the quantity of the mixture will be x + y.

Now, this mixture is Tk 64.50 per kg.
Hence, the total price of the mixture = Tk 64.50(x + y)

So, 62x + 72y = 64.50 (x+y)
⇒ 62x + 72y = 64.5x + 64.5y
⇒ 64.5x - 62x = 72y - 64.5y
⇒ 2.5x = 7.5y
⇒ x/y ​= 7.5​/2.5
⇒ x/y ​= 3
So, x : y = 3 : 1

Hence, the required ratio is 3:1.