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The image shows a mathematical word problem written in Hindi. Here's the transcription of the problem:

**Problem:**
"एक आदमी अपनी आय का 40% खर्च करता है। जीवित रहने के लिए भोजन में खर्च हुए तिहाई के साथ उसी बची हुई राशि में 3+1/3 का वृद्धि होती है। उसके उसी आय में 16 रू. की वृद्धि होती है। वह राशि कितनी थी?"

**Translation:**
"A man spends 40% of his income. For food expenses, 1/3 of the remaining amount plus an increase of \(3 + \frac{1}{3}\). There is an increase of ₹16 in his income. What was the original amount?"

### Breakdown of the Problem:

1. The man spends 40% of his income. 
2. He uses 1/3 of the remaining amount on food.
3. There is an increase of \(3 + \frac{1}{3}\) in the remaining amount.
4. The increase results in ₹16 more in his income.

Let me solve this for you step by step.

Let the original income be \( x \).

1. **Expenses:** 
   - The man spends 40%, so the remaining income is \( 60\% \) of \( x \), which is \( 0.6x \).

2. **Food Expenses:**
   - He spends \( \frac{1}{3} \) of \( 0.6x \) on food. This means the food expense is \( \frac{1}{3} \times 0.6x = 0.2x \).
   
3. **Remaining Income After Food:** 
   - The remaining amount after food expenses is \( 0.6x - 0.2x = 0.4x \).
   
4. **Increase:** 
   - The remaining amount increases by \( 3 + \frac{1}{3} \), i.e., \( 3 \frac{1}{3} = \frac{10}{3} \).
   - The total increase is ₹16, so the relation becomes:
   \[
   \frac{10}{3} \times 0.4x = 16
   \]
   
5. **Solve for \( x \):**
   Now we can solve for \( x \) from the equation.

Let me calculate this next.The original income of the man was ₹12.

Would you like a more detailed explanation or have any other questions?

Here are some related questions you might find useful:

1. What would happen if his expenses were 50% instead of 40%?
2. How would the equation change if the increase in income was ₹20 instead of ₹16?
3. Can you determine the man's total expenses if he increases his food spending by ₹5?
4. What would the total food expense be if his income doubled?
5. If the increase \(3 + \frac{1}{3}\) was replaced by a fixed ₹10, what would the new income be?

**Tip:** When solving word problems, it's often helpful to translate each part into mathematical equations to simplify the solution process!

A man spends 40% of his income. For food expenses, he uses 1/3 of the remaining amount plus an increase of 3 + 1/3. His income increased by ₹16. What was the original income?

Learn how to solve a real-life word problem involving percentages and linear equations. This problem helps you find the original income of a man who spends 40% of his earnings and has a specific increase of ₹16. Suitable for students in Grades 8-10.

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