Question
Download Solution PDF280 litres of mixture contains alcohol and water in the ratio of 4:3. If x litres of water is added to the mixture, the ratio of the quantity of alcohol to water becomes 8:7. Find the value of x.
Answer (Detailed Solution Below)
Detailed Solution
Download Solution PDFGiven:
Total mixture = 280 liters
Initial ratio of alcohol to water = 4:3
New ratio of alcohol to water after adding x liters of water = 8:7
Formula used:
Alcohol in the mixture =
Water in the mixture =
New amount of water = 120 + x liters
Calculations:
According to the problem:
⇒ 7 × 160 = 8 × (120 + x)
⇒ 1120 = 960 + 8x
⇒ 8x = 160
⇒ x = 20 liters
∴ The correct answer is x = 20 liters.
Shortcut Trick
(4 : 3 ) × 2 = (8 : 6) [multiply by 2 to keep the quantity of alcohol unchanged.]
New ratio = 8 : 7
Change in units of water = (7 - 6) = 1 unit
(8 + 6) units = 280 L ⇒ 14 units = 280 L
⇒ 1 unit = 20 L (Quantity of water added)
∴ The quantity of water to be added is 20 L.
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