Four yoga trainers A, B, C & D take
classes in a month. Pie chart shows total hours distribution
taken by these all four trainers to take classes. Read the
data carefully and answer the questions.

![image.png](https://res.cloudinary.com/aptidude/image/upload/v1756139564/aptidude_questions/e9aep4o8ontmmia2ujio.png)

Note:
(i) They take classes for 1 hour (Basic classes), 2 hours
(Regular classes) and 3 hours (Advance classes). No
trainer can leave class before time and can not take
class for any extra time.
(ii) D does not take any regular classes. He will take either
basic or advance class.

Next month D takes 10 hours classes and he use three
hours at same pattern as previous month. If number of
basic classes taken by D in next month is twice the
advance classes, then find the difference between basic
and advance classes taken by him in next month?

Question

Four yoga trainers A, B, C & D take
classes in a month. Pie chart shows total hours distribution
taken by these all four trainers to take classes. Read the
data carefully and answer the questions.

![image.png](https://res.cloudinary.com/aptidude/image/upload/v1756139564/aptidude_questions/e9aep4o8ontmmia2ujio.png)

Note:
(i) They take classes for 1 hour (Basic classes), 2 hours
(Regular classes) and 3 hours (Advance classes). No
trainer can leave class before time and can not take
class for any extra time.
(ii) D does not take any regular classes. He will take either
basic or advance class.

Next month D takes 10 hours classes and he use three
hours at same pattern as previous month. If number of
basic classes taken by D in next month is twice the
advance classes, then find the difference between basic
and advance classes taken by him in next month?

Accepted Answer

**Solution:**

1. Total hours for all trainers = 60 hours.

2. Hours taken by D = 50% of 60 = $0.50 	imes 60 = 30$ hours.

3. D only takes Basic (1 hour) and Advance (3 hours) classes, no Regular (2 hours) classes.

4. Let the number of Basic classes taken by D be $x$ and Advance classes be $y$.

Then, total hours for D:
   $$1 	imes x + 3 	imes y = 30$$

5. From the problem, the ratio of Basic to Advance classes for D in the previous month is the same as next month.

6. In the next month, D takes 10 hours of classes, with Basic classes twice the number of Advance classes:
   $$x' = 2y'$$

Total hours next month:
   $$1 	imes x' + 3 	imes y' = 10$$

Substitute $x' = 2y'$:
   $$2y' + 3y' = 10 \Rightarrow 5y' = 10 \Rightarrow y' = 2$$

Then, $x' = 2 	imes 2 = 4$.

7. The difference between Basic and Advance classes next month:
   $$x' - y' = 4 - 2 = 2$$

8. Since the ratio of Basic to Advance classes remains the same as previous month, we find the ratio from previous month data:

From step 4:
   $$x + 3y = 30$$

We need to find $\frac{x}{y}$.

Using the ratio from next month:
   $$\frac{x'}{y'} = \frac{4}{2} = 2$$

So, $x = 2y$.

Substitute in equation:
   $$2y + 3y = 30 \Rightarrow 5y = 30 \Rightarrow y = 6$$

Then, $x = 12$.

This confirms the ratio $x:y = 2:1$.

9. The question asks for the difference between Basic and Advance classes taken by D in the next month, which is:
   $$4 - 2 = 2$$

**Answer:** 2

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