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.

Friend	Operator	Outgoing minutes to		Incoming minutes from
		Operator Xitel	Operator Yocel	Operator Xitel	Operator Yocel
Anu	Xitel	100		50	225
Bijay	Xitel		200		125
Chetan	Yocel	50	175	250	150
Deepak	Yocel	100	150	275	100
Eshan	Yocel		100	100	375
Faruq	Yocel	0		100	150

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.

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

The correct option is 525.

Step-by-step Explanation:

To find the total duration of calls made by Anu (who uses Xitel) to friends using Yocel, we can use the principle of conservation of call minutes between the two operator groups.

1. Categorizing the Friends by Operator:
Based on the table, the friends are categorized as follows:
• Xitel Users: Anu, Bijay
• Yocel Users: Chetan, Deepak, Eshan, Faruq

2. Establishing the Equation for Call Minutes:
Any call made from a Xitel user to a Yocel user is recorded as an outgoing minute to Yocel by the Xitel caller, and simultaneously as an incoming minute from Xitel by the Yocel receiver.
Therefore, the sum of all outgoing minutes from Xitel users to Yocel users must be exactly equal to the sum of all incoming minutes received by Yocel users from Xitel users:

$$\sum \text{Outgoing minutes from Xitel to Yocel}=\sum \text{Incoming minutes to Yocel from Xitel}$$

3. Calculating the Total Incoming Minutes to Yocel from Xitel:
From the table, we sum the "Incoming minutes from Operator Xitel" for all Yocel users (Chetan, Deepak, Eshan, and Faruq):
• Chetan: 250 minutes
• Deepak: 275 minutes
• Eshan: 100 minutes
• Faruq: 100 minutes

$$\text{Total Incoming from Xitel}=250+275+100+100=725\text{ minutes}$$

4. Finding Anu's Outgoing Minutes to Yocel:
The total outgoing minutes from Xitel to Yocel is the sum of outgoing minutes to Yocel from Anu and Bijay:
• Bijay's outgoing minutes to Yocel = 200 minutes (given in the table)
• Let Anu's outgoing minutes to Yocel be $A_{\text{Yocel}}$.

Setting up the equation:

$$A_{\text{Yocel}}+200=725$$

Solving for $A_{\text{Yocel}}$:

$$A_{\text{Yocel}}=725-200=525\text{ minutes}$$

Thus, the total duration of calls made by Anu to friends having Yocel mobile numbers is 525 minutes.