Question

A 40% ethyl solution is mixed with another ethyl solution say, T of unknown concentration in the proportion 1 : 4 by volume. This mixture is then mixed with equal volume of 40% ethyl solution. The resultant mixture is a 60% ethyl solution. Find the unknown concentration of T.
1. 93.33%
2. 90%
3. 56%
4. 87%
5. 45%

Answer 1

Correct Answer - Option 2 : 90%

Concept:

By the rule of alligation :    a             b

                                                  c 

                                           x      :      y

It can be written in the following format : ax + by = c × (x + y)

Calculation: 

M1 = 40% ethyl solution is mixed with M2 = T in the ratio 1 : 4 and let their proportion be 1 unit and 4 units respectively. The total proportion (M3) after mixing this solution with equal volume of 40% ethyl solution be 10 units ( M1 = 1 unit, M2 = 4 units and M3 = 10 units )

If we observe, we have total quantity of 40% ethyl solution of 6 units  (M1 = 1 + M3 = 5 units) 

40%             T

           60%

6          :        4

40% × 6 + T × 4 = 60% × (6 + 4) 

240% + 4T = 600%

4T = 360%

∴ T = 90%