CAT 2023 - Slot 3 Dilr Question 13
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CAT 2023 Slot 3 - DILR
Suppose, A is the total number of AC's sold.
From the given information, that the total number of ACs sold in the city, 25% were of Window variant.
Window AC's = A/4 and Split AC's = 3A/4
Now, Suppose B is the total Number of inverter ACs
From the given information, that among the Inverter ACs sold, 20% were of Window variant.
Window Inverter AC's = B/5 and Window Non-Inverter AC's = 4B/5
From the given condition 3, we get
A/4 - B/5 = 6 & 4B/5 = 36
So, B = 46 and A = 60
So, From condition-6
(i) If D1 and D4 sold no window Non-inverter ACs, then D2 sold twice as many as D3, meaning D2 sold 4 and D3 sold 2 of this type.
From condition-2
(ii) Let's say D1 sold x window inverter ACs, then the number of split inverter ACs sold would be 13 minus x.
From condition-5
(iii) Let's suppose y represents the number of window ACs sold by D3 and D4. In that case, D2 sold 3y ACs of this type.
From condition-4
(iv) Number of split ACs sold by D1 will be 2x
From condition-7
(v) Let's say z represents the number of split inverter ACs sold by D3 and D4. In that case, D2 sold twice as many, totaling 2z ACs of this type.
Now, let use the (i), (ii), (iii), (iv) and (v) to create a table:
As per the question, the total number of window ACs is 15.
So, x + 3y + y + y = 15
x + 5y = 15 (where x and y should be greater than or equal to 2 from condition 1)
Hence, the only solution is x = 5 and y = 2
Now, use the values to fill the table:
So, the Number of split Inverter ACs is 36, which means that 8 + 2z + z + z = 36
4z = 28
z = 7
Now, use the value of z and using the (5), the number of split AC's sold by D1 is 2 × 5 = 10
Now, the total number of ACs sold by D2 and D4: = 60 – D1 – D3
= 60 – 15 – 12
= 33
Therefore, the correct answer is 33.