Passage

Directions: A dishonest juice seller mixed some water into pure fruit juice and sold it to four shopkeepers X, Y, Z, and W in the same order. After mixing, the ratio of juice to water became 4 : 1. The table below shows how the juice seller handled the transactions: Shopkeepers Quantity Sold (in Litres) Juice Added (in Litres) Water Added (in Litres) Mixture Left (in Litres) X 110 50 0 500 Y M 34 9 N Z 98 3r r P W 95 3r - 6 r T

If the difference between the quantities of juice and water in the mixture before selling to W is 171 liters, then find the value of r (If the ratio of juice to water just before selling to Z was 40 : 9).

Using the total mixture of 343 liters before selling to Z with a juice to water ratio of 40 : 9, the mixture contains 280 liters of juice and 63 liters of water. After selling 98 liters in this ratio to shopkeeper Z, the remaining mixture is 245 liters containing 200 liters of juice and 45 liters of water. Before selling to W, adding 3r liters of juice and r liters of water brings the total juice to 200 + 3r and the total water to 45 + r. The difference is given as 171 liters, so (200 + 3r) - (45 + r) = 171, which simplifies to 2r = 16 and r = 8.

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