The pie chart shows the income distribution of four earning members of a family as a percentage of the total family income in the year 2016:

![image.png](https://res.cloudinary.com/aptidude/image/upload/v1759327509/aptidude_questions/sxs3tzzu6hmj9fjwghfv.png)

If the incomes of B and D increased by 20% and 40% respectively in the year 2017 compared to 2016, what is the ratio of the combined income of B and D in 2016 to their combined income in 2017?

Question

The pie chart shows the income distribution of four earning members of a family as a percentage of the total family income in the year 2016:

![image.png](https://res.cloudinary.com/aptidude/image/upload/v1759327509/aptidude_questions/sxs3tzzu6hmj9fjwghfv.png)

If the incomes of B and D increased by 20% and 40% respectively in the year 2017 compared to 2016, what is the ratio of the combined income of B and D in 2016 to their combined income in 2017?

Accepted Answer

**Solution:**

1. Let the total family income in 2016 be $100$ units for simplicity.

2. Income of B in 2016 = $35\%$ of $100 = 35$ units.

3. Income of D in 2016 = $10\%$ of $100 = 10$ units.

4. Combined income of B and D in 2016 = $35 + 10 = 45$ units.

5. Income of B in 2017 after 20\% increase:
   $$35 + (20\% 	imes 35) = 35 + 7 = 42$$ units.

6. Income of D in 2017 after 40\% increase:
   $$10 + (40\% 	imes 10) = 10 + 4 = 14$$ units.

7. Combined income of B and D in 2017 = $42 + 14 = 56$ units.

8. Required ratio of combined income of B and D in 2016 to 2017:
   $$45 : 56$$

**Answer:** $45 : 56$

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