CAT 2025 Slot 3 DILR Question & Solution
Data Set
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.
Question 1
What was the duration of calls (in minutes) from Bijay to Anu?
Solution:
This is the table given in the question with unknown values of a, b, c, d and e.
We are told that Anu and Bijay use the Xitel operator, and Chetan, Deepak, Esthan and Faruq use the Yocel operator.
The outgoing call from Anu to the Xitel operator has to be the incoming call from Xitel to Bijay because there are only two friends using Xitel, and if one of the Xitel users is calling another Xitel user, then those two have to be Anu and Bijay.
The outgoing to Xitel by Anu = 100
The incoming from Xitel for Bijay = c = The outgoing to Xitel by Anu = 100
So, the value of c in the above table is 100.
The outgoing to Xitel by Bijay = b
The incoming from Xitel for Anu = 50 = The outgoing to Xitel by Bijay = b
So, the value of b in the above table is 50.
The sum of Outgoing from Anu and Bijay to operator Yocel must be equal to the sum of Incoming minutes from Xitel for Chetan, Deepak, Esthan and Faruq.
The sum of Outgoing from Anu and Bijay to operator Yocel = a + 200
The sum of Incoming minutes from Xitel for Chetan, Deepak, Esthan and Faruq = 250 + 275 + 100 + 100 = 725
Equating them, we get,
a + 200 = 725
a = 525
So, the value of a in the above table is 525.
The sum of outgoing minutes from Chetan, Deepak, Esthan, and Faruq to operator Xitel must be equal to the sum of Incoming minutes from Yocel for Anu and Bijay.
The sum of outgoing minutes from Chetan, Deepak, Esthan, and Faruq to operator Xitel = 50 + 100 + d + 0 = 150 + d
The sum of Incoming minutes from Yocel for Anu and Bijay = 225 + 125 = 350
Equating them, we get,
150 + d = 350
d = 200
So, the value of d in the above table is 200.
The sum of outgoing minutes from Chetan, Deepak, Esthan, and Faruq to operator Yocel must be equal to the sum of Incoming minutes from Yocel for Chetan, Deepak, Esthan, and Faruq.
The sum of outgoing minutes from Chetan, Deepak, Esthan, and Faruq to operator Yocel = 175 + 150 + 100 + e = 425 + e
The sum of Incoming minutes from Yocel for Chetan, Deepak, Esthan, and Faruq = 150 + 100 + 375 + 150 = 775
Equating them, we get,
425 + e = 775
e = 350
So, the value of e in the above table is 350.
The final table is,
The duration of calls from Bijay to Ajay is 50 minutes, which is the outgoing minutes to operator Xitel of Bijay.
Hence, the correct answer is 50.
Question 2
What was the total duration of calls (in minutes) made by Anu to friends having mobile numbers from Operator Yocel?
Solution:
This is the table given in the question with unknown values of a, b, c, d and e.
We are told that Anu and Bijay use the Xitel operator, and Chetan, Deepak, Esthan and Faruq use the Yocel operator.
The outgoing call from Anu to the Xitel operator has to be the incoming call from Xitel to Bijay because there are only two friends using Xitel, and if one of the Xitel users is calling another Xitel user, then those two have to be Anu and Bijay.
The outgoing to Xitel by Anu = 100
The incoming from Xitel for Bijay = c = The outgoing to Xitel by Anu = 100
So, the value of c in the above table is 100.
The outgoing to Xitel by Bijay = b
The incoming from Xitel for Anu = 50 = The outgoing to Xitel by Bijay = b
So, the value of b in the above table is 50.
The sum of Outgoing from Anu and Bijay to operator Yocel must be equal to the sum of Incoming minutes from Xitel for Chetan, Deepak, Esthan and Faruq.
The sum of Outgoing from Anu and Bijay to operator Yocel = a + 200
The sum of Incoming minutes from Xitel for Chetan, Deepak, Esthan and Faruq = 250 + 275 + 100 + 100 = 725
Equating them, we get,
a + 200 = 725
a = 525
So, the value of a in the above table is 525.
The sum of outgoing minutes from Chetan, Deepak, Esthan, and Faruq to operator Xitel must be equal to the sum of Incoming minutes from Yocel for Anu and Bijay.
The sum of outgoing minutes from Chetan, Deepak, Esthan, and Faruq to operator Xitel = 50 + 100 + d + 0 = 150 + d
The sum of Incoming minutes from Yocel for Anu and Bijay = 225 + 125 = 350
Equating them, we get,
150 + d = 350
d = 200
So, the value of d in the above table is 200.
The sum of outgoing minutes from Chetan, Deepak, Esthan, and Faruq to operator Yocel must be equal to the sum of Incoming minutes from Yocel for Chetan, Deepak, Esthan, and Faruq.
The sum of outgoing minutes from Chetan, Deepak, Esthan, and Faruq to operator Yocel = 175 + 150 + 100 + e = 425 + e
The sum of Incoming minutes from Yocel for Chetan, Deepak, Esthan, and Faruq = 150 + 100 + 375 + 150 = 775
Equating them, we get,
425 + e = 775
e = 350
So, the value of e in the above table is 350.
The final table is,
The total duration of calls made by Anu to friends having mobile numbers from Operator Yocel is Anu's outgoing minutes to Operator Yocel, which is 525 minutes.
Hence, the correct answer is 525.
Question 3
What was the total duration of calls (in minutes) made by Faruq to friends having mobile numbers from Operator Yocel?
Solution:
This is the table given in the question with unknown values of a, b, c, d and e.
We are told that Anu and Bijay use the Xitel operator, and Chetan, Deepak, Esthan and Faruq use the Yocel operator.
The outgoing call from Anu to the Xitel operator has to be the incoming call from Xitel to Bijay because there are only two friends using Xitel, and if one of the Xitel users is calling another Xitel user, then those two have to be Anu and Bijay.
The outgoing to Xitel by Anu = 100
The incoming from Xitel for Bijay = c = The outgoing to Xitel by Anu = 100
So, the value of c in the above table is 100.
The outgoing to Xitel by Bijay = b
The incoming from Xitel for Anu = 50 = The outgoing to Xitel by Bijay = b
So, the value of b in the above table is 50.
The sum of Outgoing from Anu and Bijay to operator Yocel must be equal to the sum of Incoming minutes from Xitel for Chetan, Deepak, Esthan and Faruq.
The sum of Outgoing from Anu and Bijay to operator Yocel = a + 200
The sum of Incoming minutes from Xitel for Chetan, Deepak, Esthan and Faruq = 250 + 275 + 100 + 100 = 725
Equating them, we get,
a + 200 = 725
a = 525
So, the value of a in the above table is 525.
The sum of outgoing minutes from Chetan, Deepak, Esthan, and Faruq to operator Xitel must be equal to the sum of Incoming minutes from Yocel for Anu and Bijay.
The sum of outgoing minutes from Chetan, Deepak, Esthan, and Faruq to operator Xitel = 50 + 100 + d + 0 = 150 + d
The sum of Incoming minutes from Yocel for Anu and Bijay = 225 + 125 = 350
Equating them, we get,
150 + d = 350
d = 200
So, the value of d in the above table is 200.
The sum of outgoing minutes from Chetan, Deepak, Esthan, and Faruq to operator Yocel must be equal to the sum of Incoming minutes from Yocel for Chetan, Deepak, Esthan, and Faruq.
The sum of outgoing minutes from Chetan, Deepak, Esthan, and Faruq to operator Yocel = 175 + 150 + 100 + e = 425 + e
The sum of Incoming minutes from Yocel for Chetan, Deepak, Esthan, and Faruq = 150 + 100 + 375 + 150 = 775
Equating them, we get,
425 + e = 775
e = 350
So, the value of e in the above table is 350.
The final table is,
The total duration of calls made by Faruq to friends having mobile numbers from Operator Yocel is the outgoing minutes from Faruq to Operator Yocel, which is 350 minutes.
Hence, the correct answer is 350.
Question 4
What was the duration of calls (in minutes) from Deepak to Chetan?
Solution:
This is the table given in the question with unknown values of a, b, c, d and e.
We are told that Anu and Bijay use the Xitel operator, and Chetan, Deepak, Esthan and Faruq use the Yocel operator.
The outgoing call from Anu to the Xitel operator has to be the incoming call from Xitel to Bijay because there are only two friends using Xitel, and if one of the Xitel users is calling another Xitel user, then those two have to be Anu and Bijay.
The outgoing to Xitel by Anu = 100
The incoming from Xitel for Bijay = c = The outgoing to Xitel by Anu = 100
So, the value of c in the above table is 100.
The outgoing to Xitel by Bijay = b
The incoming from Xitel for Anu = 50 = The outgoing to Xitel by Bijay = b
So, the value of b in the above table is 50.
The sum of Outgoing from Anu and Bijay to operator Yocel must be equal to the sum of Incoming minutes from Xitel for Chetan, Deepak, Esthan and Faruq.
The sum of Outgoing from Anu and Bijay to operator Yocel = a + 200
The sum of Incoming minutes from Xitel for Chetan, Deepak, Esthan and Faruq = 250 + 275 + 100 + 100 = 725
Equating them, we get,
a + 200 = 725
a = 525
So, the value of a in the above table is 525.
The sum of outgoing minutes from Chetan, Deepak, Esthan, and Faruq to operator Xitel must be equal to the sum of Incoming minutes from Yocel for Anu and Bijay.
The sum of outgoing minutes from Chetan, Deepak, Esthan, and Faruq to operator Xitel = 50 + 100 + d + 0 = 150 + d
The sum of Incoming minutes from Yocel for Anu and Bijay = 225 + 125 = 350
Equating them, we get,
150 + d = 350
d = 200
So, the value of d in the above table is 200.
The sum of outgoing minutes from Chetan, Deepak, Esthan, and Faruq to operator Yocel must be equal to the sum of Incoming minutes from Yocel for Chetan, Deepak, Esthan, and Faruq.
The sum of outgoing minutes from Chetan, Deepak, Esthan, and Faruq to operator Yocel = 175 + 150 + 100 + e = 425 + e
The sum of Incoming minutes from Yocel for Chetan, Deepak, Esthan, and Faruq = 150 + 100 + 375 + 150 = 775
Equating them, we get,
425 + e = 775
e = 350
So, the value of e in the above table is 350.
The final table is,
Label the unknown value we need as
$$x=\text{minutes from Deepak to Chetan}$$
Use the operator groups from the table:
Xitel users: Anu, Bijay.
Yocel users: Chetan, Deepak, Eshan, Faruq.
Chetan’s incoming from Yocel = 150 minutes.
Yocel$$\to$$Chetan can come only from Deepak, Eshan, or Faruq. But the problem states Eshan $$\to$$ Chetan = 0, so
$$(\text{Deepak}\to\text{Chetan}) + (\text{Faruq}\to\text{Chetan}) = 150$$
Hence
$$x + (\text{Faruq}\to\text{Chetan}) = 150 \qquad(1)$$
Faruq’s outgoing to Yocel = 350 minutes (table). Those 350 minutes are split among Yocel recipients Chetan, Deepak and Eshan. We are told Faruq$$\to$$Eshan = 200 (given). So
$$(\text{Faruq}\to\text{Chetan}) + (\text{Faruq}\to\text{Deepak}) + 200 = 350,$$
hence
$$(\text{Faruq}\to\text{Chetan}) + (\text{Faruq}\to\text{Deepak}) = 150 \qquad(2)$$
Consider Deepak’s incoming from Yocel (table) = 100 minutes. The ones in Yocel that can call Deepak are Chetan, Eshan, and Faruq. But we are told Chetan $$\to$$ Deepak = 0 and Eshan $$\to$$ Deepak = 0, so the only Yocel caller to Deepak is Faruq. Therefore
$$(\text{Faruq}\to\text{Deepak}) = 100 \qquad(3)$$
Substitute (3) into (2):
$$(\text{Faruq}\to\text{Chetan}) + 100 = 150 \quad\Rightarrow\quad (\text{Faruq}\to\text{Chetan}) = 50.$$
Now use (1):
$$x + (\text{Faruq}\to\text{Chetan}) = 150$$.
With $$\text{Faruq}\to\text{Chetan} = 50$$, we get,
$$x + 50 = 150$$
$$x = 100$$
Thus Deepak $$\to$$ Chetan = 100 minutes.
Hence, the correct answer is option A.