Directions : Read the following table carefully and answer the questions given…

2024

Directions : Read the following table carefully and answer the questions given below. The table shows the total number of cars manufactured, the total number of cars sold, and the total number of cars unsold by four companies.

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Note: (i) Total cars unsold by D is 1/3rd of the total cars sold by the company.
(ii) Total cars sold by all the companies are 3552.

The total number of cars sold by F is (7X+Z+12)/2 and the total number of cars unsold by F is 2P. Find which of the following option is correct about the difference between the total cars manufactured by F and A & C together.

  1. A.

    5P/3

  2. B.

    2(P-X)

  3. C.

    (X+Z)/3

  4. D.

    X+146

  5. E.

    P -258

Show answer & explanation

Correct answer: E

Concept

In any manufactured-sold-unsold split, the three quantities are tied by one identity: Manufactured = Sold + Unsold. So an unknown manufactured count is recovered the moment its sold and unsold counts are known. A row that gives all three (like C) lets you pin a variable, and the two notes give two more equations - enough to solve for X, Z and P.

Application

  1. Pin X from row C. Row C is fully numeric in manufactured (900) and sold (648), and its unsold is 3X. By the identity, Unsold = Manufactured - Sold = 900 - 648 = 252, so 3X = 252 and X = 84.

  2. Use Note (i) for D. Unsold by D = 1/3 of Sold by D: P/3 + 150 = (1/3)(2Z + 132). Multiply by 3: P + 450 = 2Z + 132, hence P = 2Z - 318.

  3. Use Note (ii) - total sold = 3552. Sold of A + B + C + D = Z + 60/7 . X + 648 + (2Z + 132) = 3552. With X = 84, 60/7 . 84 = 720, so 3Z + 720 + 780 = 3552, giving 3Z = 2052 and Z = 684.

  4. Get P. From P = 2Z - 318 = 2(684) - 318 = 1050.

  5. Build manufactured of F. Manufactured F = Sold F + Unsold F = (7X + Z + 12)/2 + 2P. Numerically (7 . 84 + 684 + 12)/2 + 2(1050) = (588 + 684 + 12)/2 + 2100 = 1284/2 + 2100 = 642 + 2100 = 2742.

  6. Manufactured of A and C together. = Manufactured A + Manufactured C = P + 900 = 1050 + 900 = 1950.

  7. Difference. 2742 - 1950 = 792.

Cross-check

Express 792 in the variables: 792 = 1050 - 258 = P - 258, which matches the closed form. Independent check on the totals: sold A+B+C+D = 684 + 720 + 648 + 1500 = 3552 (Note ii holds), and Unsold D = P/3 + 150 = 350 + 150 = 500 = (1/3)(1500) (Note i holds). The value 792 is confirmed.

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