Mangoes are sold at Rs `43 1/2` i per kg. What is the weight of mangoes available for Rs `326 1/4` ?

Answer

To solve the problem of finding the weight of mangoes available for Rs. 326 1/4 when they are sold at Rs. 43 1/2 per kg, we can follow these steps:

### Step 1: Convert the mixed numbers into improper fractions.
- For Rs. 43 1/2:
\[ 43 \frac{1}{2} = \frac{43 \times 2 + 1}{2} = \frac{86 + 1}{2} = \frac{87}{2} \]

- For Rs. 326 1/4:
\[ 326 \frac{1}{4} = \frac{326 \times 4 + 1}{4} = \frac{1304 + 1}{4} = \frac{1305}{4} \]

### Step 2: Set up the equation to find the weight of mangoes.
- Let the weight of mangoes be \( x \) kg. The cost of \( x \) kg of mangoes can be expressed as:
\[ \text{Cost} = \text{Weight} \times \text{Price per kg} \]
Therefore,
\[ \frac{1305}{4} = x \times \frac{87}{2} \]

### Step 3: Solve for \( x \).
- Rearranging the equation gives:
\[ x = \frac{1305}{4} \div \frac{87}{2} \]
- Dividing by a fraction is the same as multiplying by its reciprocal:
\[ x = \frac{1305}{4} \times \frac{2}{87} \]
- Simplifying:
\[ x = \frac{1305 \times 2}{4 \times 87} \]
- Calculate \( 1305 \times 2 = 2610 \) and \( 4 \times 87 = 348 \):
\[ x = \frac{2610}{348} \]

### Step 4: Simplify the fraction.
- To simplify \( \frac{2610}{348} \), we can divide both the numerator and the denominator by their greatest common divisor (GCD). The GCD of 2610 and 348 is 6:
\[ x = \frac{2610 \div 6}{348 \div 6} = \frac{435}{58} \]

### Step 5: Convert the improper fraction back to a mixed number.
- Dividing 435 by 58 gives us 7 with a remainder:
\[ 435 \div 58 = 7 \quad \text{(remainder 21)} \]
- Therefore, we can express it as:
\[ x = 7 \frac{21}{58} \]

### Final Answer:
The weight of mangoes available for Rs. 326 1/4 is \( 7 \frac{21}{58} \) kg.

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