In a mixture of wheat and barley the wheat is `60%`. To 400 quintals of the mixture a quantity of barley is added and then the wheat is `53 1/3 %` of resulting mixture. How many quintals of barley are added ?

Options

A. (400)/7 quintals
B. 50 quintals
C. 46 2/3 quintals
D. 53 2/3 quintals

Answer

To solve the problem, we need to find out how many quintals of barley are added to a mixture of wheat and barley. Let's break this down step by step.

### Step 1: Calculate the amount of wheat in the initial mixture
The initial mixture consists of 400 quintals, with wheat making up 60% of it.

\[ \text{Amount of wheat} = 60\% \text{ of } 400 = \frac{60}{100} \times 400 = 240 \text{ quintals} \]

**Hint:** To find the percentage of a quantity, multiply the percentage (as a fraction) by the total quantity.

### Step 2: Set up the equation for the new mixture
Let \( y \) be the amount of barley added. After adding barley, the total amount of the mixture becomes:

\[ \text{Total mixture} = 400 + y \text{ quintals} \]

### Step 3: Set up the equation for the percentage of wheat in the new mixture
After adding \( y \) quintals of barley, the percentage of wheat in the new mixture is given as \( 53 \frac{1}{3}\% \) or \( \frac{160}{300} \) (which simplifies to \( \frac{16}{30} \) or \( \frac{8}{15} \)).

We can express this as:

\[ \frac{\text{Amount of wheat}}{\text{Total mixture}} = \frac{8}{15} \]

Substituting the known values:

\[ \frac{240}{400 + y} = \frac{8}{15} \]

### Step 4: Cross-multiply to solve for \( y \)
Cross-multiplying gives us:

\[ 240 \times 15 = 8 \times (400 + y) \]

Calculating the left side:

\[ 3600 = 3200 + 8y \]

### Step 5: Isolate \( y \)
Now, we can isolate \( y \):

\[ 3600 - 3200 = 8y \]
\[ 400 = 8y \]
\[ y = \frac{400}{8} = 50 \]

### Conclusion
The amount of barley added is \( 50 \) quintals.

**Final Answer:** 50 quintals of barley are added.

---