From a cask filled with 867 litres of wine, y litres are first drawn and replaced with water. After the first replacement the ratio of wine and water in the cask, when expressed in the lowest form, is given as a : b. From this mixture y litres are drawn and replaced with water. The ratio of wine to water in the cask after the second replacement, when expressed in the lowest form, is given as 169 : 120. Find the value of (y + a + b).

Correct option is C

Given:
Initial quantity of wine in the cask = 867 litres.
First, y litres of wine is drawn and replaced with water. After the first replacement, the ratio of wine to water is a : b.
After the second replacement, y litres are drawn again, and the ratio of wine to water becomes 169 : 120.

Solution:
The ratio of wine to total volume is $$\frac{169}{289}.$$​​
The Ratio after both replacements be:

$$= \frac{169}{289} = \left(\frac{13}{17}\right)^2$$​
Where, square denotes 2 replacement.

So, 

​$$\frac{\text{Wine}}{\text{Total Volume}}$$​ = $$\frac{13}{17}$$​​
then water Ratio = Total volume - Wine = 17 - 13 = 4 unit
Therefore a (Wine) = 13, b (Water) = 4

The total amount of wine initially in the cask is 867 litres, and after the first replacement, y litres of wine are drawn. From this:

y = $$867 \times \frac{4}{17}$$ = 204​
Calculating y + a + b.
 y = 204, a = 13, and b = 4,

y + a + b = 204 + 13 + 4 = 221
The value of y + a + b is 221

Thus, the correct option is (c) 221