A hospital uses a mixture of salt and water at Tk. 7.62/litre. This mixture contains 5% salt. Another mixture containing 75% water costs Tk. 7.82/litre. How much does the patient pay if he buys 5 litres of mixture containing 18% salt?

Question: A hospital uses a mixture of salt and water at Tk. 7.62/litre. This mixture contains 5% salt. Another mixture containing 75% water costs Tk. 7.82/litre. How much does the patient pay if he buys 5 litres of mixture containing 18% salt?

Solution:
1st mixture contains 5% salt.
2nd mixture contains 75% water i.e. 25 % salt.
Required % of salt = 18%.
∴ Required ratio = 25 - 18 : 18 - 5 = 7 : 13
and required price of the mixture = 7.82 - x : x - 7.62 = 7 : 13 [Let, patient pays Tk. x per kg]
⇒ 13(7.82 - x) = 7(x - 7.62)
⇒ 101.66 - 13x = 7x - 53.34
⇒ 20x = 155
⇒ x = 7.75
Hence price of 5 liters of this mixture = 7.75 × 5 = Tk. 38.75.