A mixture of two sugar solutions contains 26% sugar in the first solution and 60% sugar in the second solution. The overall sugar concentration in the mixture is 43%. If 150 liters of the mixture is prepared, what is the quantity (in liters) of the second solution used? If the sugar concentration of the mixture was 55%, what would have been the quantity (in liters) of the second sugar solution in the mixture? (Round off your answer to the nearest integer.)
75, 128
Case 1 (mixture at 43%): by alligation, first : second \(=(60-43):(43-26)=17:17=1:1\).
So the second solution is \(\frac{1}{2}\times150=75\) liters.
Case 2 (mixture at 55%): first : second \(=(60-55):(55-26)=5:29\).
Second solution \(=\frac{29}{34}\times150=\frac{4350}{34}\approx127.94\), which rounds to 128 liters.
So the two quantities are 75 liters and 128 liters.
Hence, the answer is 75, 128.
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