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UPSC Prelims

Mathematics

Theme:

Ratio, Proportion, Partnership and Mixture / अनुपात, समानुपात, साझेदारी और मिश्रण

Q69 2022, Ratio, Proportion, Partnership and Mixture

There are two containers X and Y. X contains 100 ml of milk and Y contains 100 ml of water. 20 ml of milk from X is transferred to Y. After mixing well, 20 ml of the mixture in Y is transferred back to X. If m denotes the proportion of milk in X and n denotes the proportion of water in Y, then which one of the following is correct?

X और Y दो पात्र हैं। X में 100 ml दूध है और Y में 100 ml पानी है। X में से 20 ml दूध निकालकर Y में डाला जाता है। इन्हें अच्छी तरह मिलाकर, Y का 20 ml मिश्रण निकालकर वापस X में मिलाया जाता है। यदि X में दूध का अनुपात m से निर्दिष्ट होता है और Y में जल का अनुपात n से निर्दिष्ट होता है, तो निम्नलिखित में से कौन-सा एक सही है?

Explanation Please wait..

Container X has 100 ml milk, and Container Y has 100 ml water.

When 20 ml milk goes from X to Y, X is left with 80 ml milk, and Y now has 100 ml water plus 20 ml milk.

So total water and milk ratio in container Y will be 5:1.

Now 20ml of the mixture of Y is transferred to X.

So, transferred amount will be 5/6 x 20 ml water and 1/6 x 20 ml milk.

Or 50/3 ml water, and 10/3 ml milk.

Thus in Y , water left = 100 - 50/3 and milk left = 20 - 10/3.

So ratio of water in Y = (100 - 50/3) / 100 = 5/6 = n (as per question)

Now container X got 20 ml of mixture in Y. So milk = 80 + 10/3 = 250/3 ml and water = 50/3

So ratio of milk in X (m) = (250/3) / 100 = 5/6
Thus, m = n.

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