Pranav had a basket of fruits. He gave one-fourth of the fruits to a friend, three-fifths to his cousin, and ate the remaining 6 fruits himself. Find the total number of fruits in the basket.

Options

A. `8`
B. `40`
C. `6`
D. `48`

Answer

To solve the problem step by step, we can follow these instructions:

### Step 1: Define the variable
Let the total number of fruits in the basket be \( x \).

### Step 2: Determine the fractions given away
Pranav gave:
- One-fourth of the fruits to a friend: \( \frac{1}{4}x \)
- Three-fifths of the fruits to his cousin: \( \frac{3}{5}x \)

### Step 3: Calculate the remaining fruits
After giving away the fruits, the remaining fruits that Pranav ate are 6. Therefore, we can set up the equation:
\[ x - \left(\frac{1}{4}x + \frac{3}{5}x\right) = 6 \]

### Step 4: Simplify the equation
First, we need to combine the fractions on the left side. To do this, we find a common denominator for \( \frac{1}{4} \) and \( \frac{3}{5} \). The least common multiple (LCM) of 4 and 5 is 20.

Convert the fractions:
- \( \frac{1}{4}x = \frac{5}{20}x \)
- \( \frac{3}{5}x = \frac{12}{20}x \)

Now substitute these back into the equation:
\[ x - \left(\frac{5}{20}x + \frac{12}{20}x\right) = 6 \]

Combine the fractions:
\[ x - \frac{17}{20}x = 6 \]

### Step 5: Solve for \( x \)
Now, simplify the left side:
\[ \frac{20}{20}x - \frac{17}{20}x = 6 \]
\[ \frac{3}{20}x = 6 \]

To isolate \( x \), multiply both sides by \( \frac{20}{3} \):
\[ x = 6 \times \frac{20}{3} \]
\[ x = \frac{120}{3} \]
\[ x = 40 \]

### Conclusion
The total number of fruits in the basket is \( 40 \).

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