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Mixture Replacement Ratio

CAT 2022 Slot 3 · Quantitative Ability · Easy · Arithmetic

This is an easy Quantitative Ability question from the CAT 2022 Slot 3 paper. It tests Arithmetic. The full answer key and a step-by-step explanation are below — try it yourself first, then reveal the solution.

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A glass contains 500 cc of milk and a cup contains 500 cc of water. From the glass, 150 cc of milk is transferred to the cup and mixed thoroughly. Next, 150 cc of this mixture is transferred from the cup to the glass. Now, the amount of water in the glass and the amount of milk in the cup are in the ratio

  1. A.

    3 : 10

  2. B.

    10 : 3

  3. C.

    1 : 1

  4. D.

    10 : 13

Answer

C

Explanation

Initial volumes in both containers are equal (500 cc500\text{ cc} each). Since equal volumes (150 cc150\text{ cc}) are transferred back and forth, the final total volume in both containers remains equal to 500 cc500\text{ cc}.

Let WgW_g be water in glass and McM_c be milk in cup. Total water =500 cc=Wg+Wc= 500\text{ cc} = W_g + W_c. Total volume in cup =500 cc=Mc+Wc= 500\text{ cc} = M_c + W_c.

Subtracting the two equations: Wg−Mc=0  ⟹  Wg=McW_g - M_c = 0 \implies W_g = M_c

Thus, the ratio of water in the glass to milk in the cup is 1:11 : 1.

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