85% and 92% alcoholic solutions are mixed to get 35 litres of an 89% alcoholic solution. How many litres of each solution are there in the new mixture?
(a)10 of the first and 25 of the second
(b)20 of the first and 15 of the second
(c)15 of the first and 20 of the second
(d)12 of the first and 23 of the second
Answer
Answer (as printed): C
Explanation
Let x litres of the first and (35 – x) litres of the second solution be mixed together. Then, 85% of x + 92% of (35 – x) = 89% of 35 ⇒ 85x + 92 (35 – x) = 89 × 35 ⇒ 85x + 3220 – 92x = 3115 ⇒ 7x = 105 ⇒ x = 15. Hence, quantity of first solution = 15 litres ; quantity of second solution = 20 litres.
Explanation as extracted from the printed page; notation may be imperfect.