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In 540 litres solution of acid and water, the ratio of acid and water is 2 : 10. How many litres of acid must be added to it to get the solution in wh
Question

In 540 litres solution of acid and water, the ratio of acid and water is 2 : 10. How many litres of acid must be added to it to get the solution in which the ratio of acid and water is 9 : 5?

A.

719

B.

721

C.

720

D.

718

Correct option is C

Given:
Total volume of solution = 540 litres
Initial ratio of acid to water = 2 : 10
Final ratio of acid to water = 9 : 5
Formula Used:
Quantity = RatioTotal Ratio \frac{Ratio}{Total\ Ratio}​ × Total Quantity
Solution:
Initial ratio of acid to water = 2 : 10 = 1 : 5
Total ratio units = 1 + 5 = 6
Initial quantity of acid = 16 \frac{1}{6}​ × 540 = 90
Initial quantity of water = 56\frac{5}{6}​ × 540 = 450
Let the quantity of acid added be x.
New quantity of acid = 90 + x
The quantity of water remains the same = 450
New ratio = 90+x450=95\frac{90 + x}{450} = \frac{9}{5}​​
5 × (90 + x) = 9 × 450
450 + 5x = 4050
5x = 3600
x = 36005 \frac{3600}{5}​​
x = 720
Final Answer
So the correct answer is (c)

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