Improve the underlined phrasal verb in the sentence: "We will take care of your children when you are away at Mumbai."

Introduction / Context:
This sentence improvement question focuses on choosing the most natural phrasal verb in British and Indian English. The sentence promises that the speaker will watch over someone's children when the person is away. While take care of is acceptable, the exam expects you to choose the phrasal verb that best fits the context and options provided.

Given Data / Assumptions:
The original sentence is:

• We will take care of your children when you are away at Mumbai.

The options related to the underlined part are:

• be looking for
• look after
• take care after
• No improvement

Concept / Approach:
To look after someone means to take care of that person, especially children or dependants. It is a common and idiomatic phrasal verb. The phrase be looking for means to search for something. Take care after is not a standard expression. Although take care of is correct English, the examination setter wants you to replace the underlined part with the best given alternative, which is look after.

Step-by-Step Solution:
Step 1: Identify the intended meaning: to look after or care for the children in the absence of their parents. Step 2: Examine be looking for. This means to search for or try to find, which does not fit the idea of caring for children. Step 3: Examine look after. This phrasal verb directly means to take care of someone or something, especially children. Step 4: Examine take care after. This combination is not idiomatic in English and would be considered incorrect. Step 5: Examine No improvement. While take care of is grammatically correct, the test expects selection among the provided options. Look after is a perfect and standard choice. Step 6: Therefore, look after is the best and correct replacement.

Verification / Alternative check:
Read the improved sentence: We will look after your children when you are away in Mumbai. This version is fully natural and clearly expresses the promise to care for the children. In many textbooks and dictionaries, look after is given as a direct synonym for take care of, especially in British and Indian English usage.

Why Other Options Are Wrong:
Be looking for is wrong because it changes the meaning to searching, which is not the intended sense. Take care after is wrong because it is not a recognised phrasal verb in English. No improvement is not the expected answer because the exam is specifically asking you to choose an alternative that improves the sentence within the options. Look after is the accepted improved form in this context.

Common Pitfalls:
Students may be tempted to pick No improvement because take care of is familiar and correct. However, examination patterns often prefer replacing a multi word phrase with a more compact and idiomatic phrasal verb when such an option is clearly available. Another pitfall is not noticing that take care after is incorrect and assuming all combinations with take care must be valid. Always check if the suggested phrase is something you have actually encountered in standard texts.

Final Answer:
The correct improvement is look after.