CAT 2024 Slot 1 QA Q13 Equations

Question 13 of the Quantitative Ability (QA) section, CAT 2024 Slot 1, with CAT's official answer and a worked solution.

A shop wants to sell a certain quantity (in kg) of grains. It sells half the quantity and an additional 3 kg of these grains to the first customer. Then, it sells half of the remaining quantity and an additional 3 kg of these grains to the second customer. Finally, when the shop sells half of the remaining quantity and an additional 3 kg of these grains to the third customer, there are no grains left. The initial quantity, in kg, of grains is
  1. A
    18
  2. B
    36
  3. C
    50
  4. D
    42

Answer: (D) 42 Equations MCQ

Solution

  1. Work backwards. Before the third customer: half of \(R\) plus 3 = all of \(R\), so \(R = 6\).
  2. Before the second customer: after selling half + 3, 6 kg remained: \(\frac{R_2}{2} - 3 = 6 \Rightarrow R_2 = 18\).
  3. Initially: \(\frac{Q}{2} - 3 = 18 \Rightarrow Q = 42\).

Shortcut. The reverse step is 'add 3, then double': \(0 \to 6 \to 18 \to 42\).

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