Anu, Bijay, Chetan, Deepak, Eshan, and Faruq are six friends. Each of them uses a mobile number from exactly one of the two mobile operators - Xitel and Yocel. During the last month, the six friends made several calls to each other.

Each call was made by one of these six friends to another. The table below summarizes the number of minutes of calls that each of the six made to (outgoing minutes) and received from (incoming minutes) these friends, grouped by the operators. Some of the entries are missing.

It is known that the duration of calls from Faruq to Eshan was 200 minutes.

Also, there were no calls from:

i. Bijay to Eshan,

ii. Chetan to Anu and Chetan to Deepak,

iii. Deepak to Bijay and Deepak to Faruq,

iv. Eshan to Chetan and Eshan to Deepak.

Q) What was the total duration of calls (in minutes) made by Faruq to friends having mobile numbers from Operator Yocel?

The correct answer is 350.

To find the total duration of calls (in minutes) made by Faruq to friends using Operator Yocel, we must determine the individual operators of each friend and then analyze the incoming and outgoing call statistics provided in the table.

Step 1: Identify Operator Groups
Based on the table, we group the six friends by their mobile operators:

• Operator Xitel: Anu, Bijay
• Operator Yocel: Chetan, Deepak, Eshan (listed as Esthan), Faruq

Step 2: Note the Constraints and Given Call Durations
From the problem description, we have the following call durations and restrictions:

• Calls from Faruq to Eshan = 200 minutes
• Bijay to Eshan = 0 minutes
• Chetan to Anu = 0 minutes, Chetan to Deepak = 0 minutes
• Deepak to Bijay = 0 minutes, Deepak to Faruq = 0 minutes
• Eshan to Chetan = 0 minutes, Eshan to Deepak = 0 minutes

Step 3: Analyze Eshan's Outgoing and Faruq's Incoming Calls
According to the table, Eshan has 100 outgoing minutes to Operator Yocel. Since Eshan makes 0 minutes of calls to Chetan and Deepak, all of Eshan's outgoing minutes to Yocel must go to Faruq:
$$\text{Eshan to Faruq}=100\text{minutes}$$
Faruq's incoming minutes from Operator Yocel is 150. These incoming minutes are received from Chetan, Deepak, and Eshan:
$$\text{Incoming to Faruq from Yocel}=\text{Chetan to Faruq}+\text{Deepak to Faruq}+\text{Eshan to Faruq}=150$$
Since we are given that Deepak to Faruq = 0 and Eshan to Faruq = 100:
$$\text{Chetan to Faruq}+0+100=150\Rightarrow \text{Chetan to Faruq}=50\text{minutes}$$

Step 4: Analyze Chetan's Outgoing and Eshan's Incoming Calls
Chetan's outgoing minutes to Operator Yocel is 175. Since Chetan to Deepak = 0:
$$\text{Chetan to Eshan}+\text{Chetan to Faruq}=175$$
Substituting Chetan to Faruq = 50:
$$\text{Chetan to Eshan}+50=175\Rightarrow \text{Chetan to Eshan}=125\text{minutes}$$
Eshan's incoming minutes from Operator Yocel is 375. These incoming minutes are received from Chetan, Deepak, and Faruq:
$$\text{Chetan to Eshan}+\text{Deepak to Eshan}+\text{Faruq to Eshan}=375$$
Since Chetan to Eshan = 125 and Faruq to Eshan = 200:
$$125+\text{Deepak to Eshan}+200=375$$
$$325+\text{Deepak to Eshan}=375\Rightarrow \text{Deepak to Eshan}=50\text{minutes}$$

Step 5: Analyze Deepak's Outgoing and Chetan's Incoming Calls
Deepak's outgoing minutes to Operator Yocel is 150. Since Deepak to Faruq = 0:
$$\text{Deepak to Chetan}+\text{Deepak to Eshan}=150$$
Substituting Deepak to Eshan = 50:
$$\text{Deepak to Chetan}+50=150\Rightarrow \text{Deepak to Chetan}=100\text{minutes}$$
Chetan's incoming minutes from Operator Yocel is 150. Since Eshan to Chetan = 0:
$$\text{Deepak to Chetan}+\text{Faruq to Chetan}=150$$
Substituting Deepak to Chetan = 100:
$$100+\text{Faruq to Chetan}=150\Rightarrow \text{Faruq to Chetan}=50\text{minutes}$$

Step 6: Analyze Deepak's Incoming Calls from Yocel
Deepak's incoming minutes from Operator Yocel is 100. These incoming minutes are received from Chetan, Eshan, and Faruq. Since Chetan to Deepak = 0 and Eshan to Deepak = 0:
$$\text{Faruq to Deepak}=100\text{minutes}$$

Step 7: Calculate the Total Outgoing Calls from Faruq to Yocel Users
The friends using Operator Yocel are Chetan, Deepak, and Eshan. We calculate the sum of calls from Faruq to these three friends:
$$\text{Total Duration}=\text{Faruq to Chetan}+\text{Faruq to Deepak}+\text{Faruq to Eshan}$$
$$\text{Total Duration}=50+100+200=350\text{minutes}$$