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 duration of calls (in minutes) from Deepak to Chetan?
Correct Answer :
100
Solution :
The correct answer is 100.
Based on the table in the image, we can identify the operator used by each of the six friends:
• Xitel: Anu and Bijay
• Yocel: Chetan, Deepak, Eshan (written as Esthan in the table), and Faruq
Let the duration of the call from person A to person B be represented as .
From the problem description, we have the following constraints:
• Call duration from Faruq to Eshan:
• No call from Bijay to Eshan:
• No calls from Chetan to Anu and Chetan to Deepak:
and
• No calls from Deepak to Bijay and Deepak to Faruq:
and
• No calls from Eshan to Chetan and Eshan to Deepak:
and
We want to find the value of .
Step 1: Determine the total outgoing minutes from Faruq to Yocel operator users
First, we note that the total outgoing minutes from all Yocel users to other Yocel users must equal the total incoming minutes received by all Yocel users from other Yocel users.
Using the table data:
• Sum of Outgoing minutes to Yocel:
• Sum of Incoming minutes from Yocel:
Equating these two sums gives:
Therefore, the sum of outgoing calls from Faruq to other Yocel users is:
Since
, we obtain:
Step 2: Determine Eshan's outgoing minutes to Faruq
From the table, Eshan's outgoing minutes to Yocel users is 100:
Since
and
, we have:
Step 3: Analyze Faruq's incoming minutes from Yocel users
From the table, Faruq's incoming minutes from Yocel users is 150:
Given that
and
(from Step 2), we find:
Step 4: Find Chetan's outgoing minutes to Eshan
From the table, Chetan's outgoing minutes to Yocel users is 175:
Since
and
(from Step 3), we have:
Step 5: Determine Deepak's outgoing minutes to Eshan
From the table, Eshan's incoming minutes from Yocel users is 375:
Substituting
and
gives:
Step 6: Calculate Deepak's call duration to Chetan
From the table, Deepak's outgoing minutes to Yocel users is 150:
Substituting
and
, we obtain:
Thus, the duration of calls from Deepak to Chetan is 100 minutes.
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