Three vessels A, B and C contain 48 litre, X litre and 40 litre,
| Three vessels A, B and C contain 48 litre, X litre and 40 litre, respectively of mixture of acid and water. The ratio of acid and water in these vessels is 5:3, 2:1 and 3:2, respectively. If all the solution are mixed together, the ratio of acid to water in the final mixture will be 39: 23. Find the value of X?
A. 40
B. 32
C. 36
D. 45
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Right Answer is: C
SOLUTION
The quantity of acid in vessel A = \(\frac{5}{8} \times 48\) = 30 litre
The quantity of water in vessel A = \(\frac{3}{8} \times 48\) = 18 litre
The quantity of acid in vessel B = \(\frac{{2X}}{3}\) litre
The quantity of water in vessel B = \(\frac{X}{3}\) litre
The quantity of acid in vessel C = \(\frac{3}{5} \times 40\) = 24 litre
The quantity of water in vessel C = \(\frac{2}{5} \times 40\) = 16 litre
According to question,
\(\frac{{30 + \frac{{2X}}{3} + \;24}}{{18 + \frac{X}{3} + 16}} = \frac{{39}}{{23}}\)
\( \Rightarrow \frac{{162 + 2X}}{{102 + X}} = \frac{{39}}{{23}}\)
⇒ 3726 + 46X = 3978 + 39X
⇒ 46X – 39X = 252
⇒ 7X = 252
⇒ X = 252/7
⇒ X = 36