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Two equal glasses filled with mixtures of milk and water in the proportions of 2 : 1 and 1 : 1 respectively were emptied into third glass. What is the proportion of milk and water in the third glass?
- A5 : 7
- B7 : 5
- C7 : 6
- D6 : 7
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Discussion 1
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CCommunity
⇒ Let the quantity of milk and water in 1st and 2nd vessel be 2x, x and x, x respectively.
⇒ Milk in the first mixture = 2x/(2x + x) = 2/3
⇒ Water in the first mixture = x/(2x + x) = 1/3
⇒ Milk in the Second mixture = x/(x + x) = 1/2
⇒ Water in the second mixture = x/(x + x) = 1/2
⇒ Ratio of Milk and water in new mixture = (2/3 + 1/2)/(1/3 + 1/2)
⇒ Ratio of Milk and water in new mixture = {(2 × 2 + 1 × 3)/6}/{(2 × 1 + 3 × 1)/6}
⇒ Ratio of Milk and water in new mixture = (7)/(5)
∴ Ratio of Milk and water in new mixture = 7 : 5
⇒ Milk in the first mixture = 2x/(2x + x) = 2/3
⇒ Water in the first mixture = x/(2x + x) = 1/3
⇒ Milk in the Second mixture = x/(x + x) = 1/2
⇒ Water in the second mixture = x/(x + x) = 1/2
⇒ Ratio of Milk and water in new mixture = (2/3 + 1/2)/(1/3 + 1/2)
⇒ Ratio of Milk and water in new mixture = {(2 × 2 + 1 × 3)/6}/{(2 × 1 + 3 × 1)/6}
⇒ Ratio of Milk and water in new mixture = (7)/(5)
∴ Ratio of Milk and water in new mixture = 7 : 5