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A solution contains a mixture of acid and base in the ratio 17 : 3.How much fraction of the mixture must be drawn off and substituted by the base so that the ratio of acid and base in the resultant mixture in the solution becomes 1 : 1?

A solution contains a mixture of acid and base in the ratio 17 : 3.How much fraction of the mixture must be drawn off and substituted by the base so that the ratio of acid and base in the resultant mixture in the solution becomes 1 : 1? Correct Answer 7/17

Given:

Initial ratio of acid and base = 17 : 3

Final mixture of acid and base = 1 : 1

Calculation:

Let us take the acid 17x litres and 3x litres

Total mixture = 20x

let the drawn part of the mixture be y

According to the question

Acid in (20 - x) litres mixture = (17/20) × (20 - x)

⇒ 17 - 17x/20 = (340 - 17x)/20      ----(i)

on adding x litres of base, base in mixture = (3/20) × (20 - x) + x

⇒ 3 - 3x/20 + x = (60 + 17x)/20      ----(ii)

the ratio of resultant mixture = 1 : 1

equating the (I) and (ii) in the ratio 1 : 1

(340 - 17x)/20  × 1 = 1 ×  (60 + 17x)/20

340 - 17x = 60 + 17x 

34x = 280

x = 280/34 ⇒ 140/17

the required ratio = (140/17)/20 = 140/340 ⇒ 7/17

∴ 7/17 fraction of the mixture must be drawn off and substituted by the base so that the ratio of acid and base in the resultant mixture in the solution becomes  1 : 1

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