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 ratio of juice to water just before selling to Z was 40 : 9, then find the total quantity of mixture just before selling to Z.

The mixture left after shopkeeper X is 500 liters, and before selling to Y, 34 liters of juice and 9 liters of water are added, making the total mixture 543 liters. Shopkeeper Y is sold M liters, and before selling to Z, the ratio of juice to water is 40 : 9, meaning the total mixture must be a multiple of 49. Testing the options for the total mixture before selling to Z by subtracting them from 543 reveals that 343 leaves exactly 200 liters to be sold to Y. Therefore, the total quantity of mixture just before selling to Z is 343 liters.

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