The concentration of three acids, P, Q and R, is given as 15%, 25% and 35%, respectively. They are mixed in the ratio of x : 3 : 5, resulting in a 28% concentration solution. What is the value of x?

Correct option is A

Given:

Concentration of three acids are 15%, 25% and 35%

Resulting concentration =28%

Acids mixed in the ratio = x : 3 : 5

Formula Used:

Ratio concepts used

Solution:

Assume that acids a, b and c are mixed in the ratio 10kx ,30k and 50k

Total mixture =$$10kx +30k+50k = 10k(x+3+5) = 10k(x+8)$$​​

Acids are:

​$$a= \frac{15}{100}\times 10kx = 1.5kx$$​​

​$$b= \frac{25}{100} \times 30k = 7.5k$$​​

​$$c= \frac{35}{100} \times 50k = 17.5k$$​​

Total acid =$$1.5kx +7.5k +17.5k = k(1.5x+25)$$​​

Resultant is 28% mixture:

​$$\frac{k(1.5x+25)}{10k(x+8)} =\frac{28}{100}$$​​

​$$100 (1.5x+25) = 280(x+8)$$​​

​$$150x+2500 = 280x + 2240$$​​

​$$2500-2240 = 280x- 150x$$​

​$$260 = 130x$$​​

​$$x= 2$$​​