In a mobileshop `7/12` mobiles are imported and rest are manufactured in India. Further `1/5th` Indian mobiles are coloured while `5/7th` imported mobiles are black and white. If there are total 150 coloured mobiles in his shop, then total number of mobile phones in his shop is :

Options

A. 500
B. 600
C. 800
D. data insufficient

Answer

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

### Step 1: Determine the fractions of imported and Indian mobiles
Given that \( \frac{7}{12} \) of the mobiles are imported, the remaining fraction of mobiles that are manufactured in India is:
\[ 1 - \frac{7}{12} = \frac{5}{12} \]
So, \( \frac{5}{12} \) of the mobiles are Indian.

### Step 2: Define the total number of mobiles
Let the total number of mobiles in the shop be \( x \).

### Step 3: Calculate the number of imported and Indian mobiles
The number of imported mobiles is:
\[ \text{Imported mobiles} = \frac{7}{12}x \]
The number of Indian mobiles is:
\[ \text{Indian mobiles} = \frac{5}{12}x \]

### Step 4: Calculate the number of coloured mobiles
According to the problem, \( \frac{1}{5} \) of the Indian mobiles are coloured. Therefore, the number of coloured Indian mobiles is:
\[ \text{Coloured Indian mobiles} = \frac{1}{5} \times \frac{5}{12}x = \frac{1}{12}x \]

For the imported mobiles, \( \frac{5}{7} \) of them are black and white, which means the remaining \( \frac{2}{7} \) are coloured. Thus, the number of coloured imported mobiles is:
\[ \text{Coloured Imported mobiles} = \frac{2}{7} \times \frac{7}{12}x = \frac{1}{6}x \]

### Step 5: Calculate the total number of coloured mobiles
The total number of coloured mobiles in the shop is the sum of coloured Indian and coloured imported mobiles:
\[ \text{Total coloured mobiles} = \frac{1}{12}x + \frac{1}{6}x \]

To add these fractions, we need a common denominator:
\[ \frac{1}{12}x + \frac{1}{6}x = \frac{1}{12}x + \frac{2}{12}x = \frac{3}{12}x = \frac{1}{4}x \]

### Step 6: Set up the equation based on the given information
We know that the total number of coloured mobiles is 150:
\[ \frac{1}{4}x = 150 \]

### Step 7: Solve for \( x \)
To find \( x \), multiply both sides by 4:
\[ x = 150 \times 4 = 600 \]

### Conclusion
The total number of mobile phones in the shop is \( 600 \).