If `(3)/(4)` of a number is 7 more than `(1)/(6)` of the number then `(5)/(3)` of the number is :

Options

A. 12
B. 20
C. 15
D. 18

Answer

To solve the problem step by step, we will follow these steps:

### Step 1: Define the variable
Let the number be represented as \( x \).

### Step 2: Write the equation based on the problem statement
According to the problem, \( \frac{3}{4} \) of the number is 7 more than \( \frac{1}{6} \) of the number. We can write this as:
\[ \frac{3}{4}x = \frac{1}{6}x + 7 \]

### Step 3: Eliminate the fractions
To eliminate the fractions, we can find the least common multiple (LCM) of the denominators, which are 4 and 6. The LCM of 4 and 6 is 12. We will multiply the entire equation by 12:
\[ 12 \left(\frac{3}{4}x\right) = 12 \left(\frac{1}{6}x\right) + 12 \cdot 7 \]
This simplifies to:
\[ 9x = 2x + 84 \]

### Step 4: Solve for \( x \)
Now, we will isolate \( x \) by subtracting \( 2x \) from both sides:
\[ 9x - 2x = 84 \]
\[ 7x = 84 \]
Now, divide both sides by 7:
\[ x = \frac{84}{7} = 12 \]

### Step 5: Find \( \frac{5}{3} \) of the number
Now that we have found the number \( x = 12 \), we need to find \( \frac{5}{3} \) of this number:
\[ \frac{5}{3} \times 12 \]
This can be calculated as:
\[ \frac{5 \times 12}{3} = \frac{60}{3} = 20 \]

### Final Answer
Thus, \( \frac{5}{3} \) of the number is \( 20 \).

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