CAT 2025 Slot 3 · DILR · Question 21
CAT 2025 Slot 3 previous year question on Reasoning Based DI, with the answer and a step-by-step solution.
Set 5: Calls Between Six Friends — this question belongs to a set. Read the full set with all 4 questions →
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 Faruq to friends having mobile numbers from Operator Yocel?
Answer & solution
Answer: 350
Work out the calls into each Yocel user from other Yocel users.
Deepak's incoming from Yocel (100): Chetan → Deepak and Eshan → Deepak are zero, so Faruq → Deepak = 100.
Eshan's outgoing to Yocel (100): Eshan → Chetan and Eshan → Deepak are zero, so Eshan → Faruq = 100.
Faruq's incoming from Yocel (150) = Chetan → Faruq + Eshan → Faruq (100) (Deepak → Faruq is zero), so Chetan → Faruq = 50.
Chetan's outgoing to Yocel (175) = Chetan → Eshan + Chetan → Faruq (Chetan → Deepak is zero), so Chetan → Eshan = 125.
Eshan's incoming from Yocel (375) = Chetan → Eshan (125) + Deepak → Eshan + Faruq → Eshan (200), so Deepak → Eshan = 50.
Deepak's outgoing to Yocel (150) = Deepak → Chetan + Deepak → Eshan (50), so Deepak → Chetan = 100.
Chetan's incoming from Yocel (150) = Deepak → Chetan (100) + Faruq → Chetan (Eshan → Chetan is zero), so Faruq → Chetan = 50.
Faruq's outgoing to Yocel = Faruq → Chetan (50) + Faruq → Deepak (100) + Faruq → Eshan (200) = 350.
Shortcut: start with the rows where all but one sender or receiver is ruled out (Deepak's incoming and Eshan's outgoing), and the rest follows step by step.
Hence, the answer is 350.
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