Two community kitchens K1 and K2 prepare 60 and 40 meal boxes a day respectively. Three schools A, B and C need 30, 40 and 30 boxes a day respectively. Kitchen K1 sends x boxes to A and y boxes to B, and sends the rest of its boxes to C. All the boxes are sent and every school gets exactly what it needs. Match each quantity in List-I with its expression in List-II.
| List-I | List-II | ||
|---|---|---|---|
| (A) | Boxes sent from K1 to C | (I) | \(40 - y\) |
| (B) | Boxes sent from K2 to A | (II) | \(x + y - 30\) |
| (C) | Boxes sent from K2 to B | (III) | \(60 - x - y\) |
| (D) | Boxes sent from K2 to C | (IV) | \(30 - x\) |
Choose the correct answer from the options given below:
Answer & explanation
Correct answer: option 1
The correct answer is Option (1) → (A)-(III), (B)-(IV), (C)-(I), (D)-(II)
In a transportation problem every other shipment is written in terms of x and y, using the supply of each kitchen and the need of each school.
(A) Boxes sent from K1 to C
K1 has 60 boxes and sends x + y of them to A and B, so it sends (III) \(60 - x - y\) to C.
(B) Boxes sent from K2 to A
A needs 30 and gets x from K1, so it gets (IV) \(30 - x\) from K2.
(C) Boxes sent from K2 to B
B needs 40 and gets y from K1, so it gets (I) \(40 - y\) from K2.
(D) Boxes sent from K2 to C
C needs 30 and gets \(60 - x - y\) from K1, so it gets
\(30 - (60 - x - y) = x + y - 30\)
from K2, which is (II). (Check: K2 sends \((30 - x) + (40 - y) + (x + y - 30) = 40\) boxes in all.)