Three glasses P, Q and R have capacities in the ratio 1 ∶ 2 ∶ 3. All these glasses are completely filled with mixtures of milk and water. The ratio of milk to water in P is 1 âˆ¶ 2, in Q it is 2 ∶ 3 and in R it is 3 âˆ¶ 1. If the content of all three glasses are put into a bigger container, what will be the ratio of milk to water in the container?

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CDS Elementary Mathematics 3 Sep 2023 Official Paper
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  1. 203 âˆ¶ 117
  2. 203 âˆ¶ 157
  3. 172 âˆ¶ 91
  4. 165 âˆ¶ 88  

Answer (Detailed Solution Below)

Option 2 : 203 âˆ¶ 157
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Detailed Solution

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Given:

Three glasses P, Q, and R have capacities in the ratio 1 ∶ 2 ∶ 3

The ratio of milk to water in P, Q & R is 1 âˆ¶ 2, 2 ∶ 3, 3 âˆ¶ 1 respectively

Calculation:

Let the quantity of mixture in P, Q & R be 1L, 2L & 3L respectively

In glass P

⇒ Quantity of Milk = 1 × (1/3) = (1/3) L

⇒ Quantity of Water = 1 × (2/3) = (2/3) L

In glass Q

⇒ Quantity of Milk = 2 × (2/5) = (4/5) L

⇒ Quantity of Water = 2 × (3/5) = (6/5) L

In glass R

⇒ Quantity of Milk = 3 × (3/4) = (9/4) L

⇒ Quantity of Water = 3 × (1/4) = (3/4) L

In Bigger Container

⇒ Quantity of Milk = \(\frac{1}{3}\) + \(\frac{4}{5}\) + \(\frac{9}{4}\) = \(\frac{20+48+135}{60}\) = \(\frac{203}{60}\)

⇒ Quantity of Water = \(\frac{2}{3}\) + \(\frac{6}{5}\) + \(\frac{3}{4}\) = \(\frac{40+72+45}{60}\) = \(\frac{157}{60}\)

∴ The ratio of milk to water in the container is 203 : 157.

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