# CAT 2021 QA - Slot 3

Get the complete CAT 2021 paper with answers and explanations

## CAT 2021 Question Paper With Answers & Explanation

### QA

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#### Q. 8 Anil can paint a house in 12 days while Barun can paint it in 16 days. Anil, Barun, and Chandu undertake to paint the house for ₹ 24000 and the three of them together complete the painting in 6 days. If Chandu is paid in proportion to the work done by him, then the amount in INR received by him is

3000

###### Explanation

Given that Anil and Barun alone can do the work in 12 days and 16 days respectively.
Along with Chandu they complete the work in 6 days.
Let the total work be 48 units (LCM of 12 and 16).
Together they do 48/6 = 8 units in one day.
Out of these 8 units Anil does 48/12 = 4 units and Barun does 48/16 = 3 units.
So work done in a day by Chandu = 8 - 7 = 1 unit, which means Chandu takes 48 days to complete the work alone.
Ratio of wages of Anil : Barun : Chandu is in proportion to the work done = 4 : 3 : 1.
Hence, Chandu’s share = ⅛ x 24000 = Rs.3,000.

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#### Q. 16 If a certain weight of an alloy of silver and copper is mixed with 3 kg of pure silver, the resulting alloy will have 90% silver by weight. If the same weight of the initial alloy is mixed with 2 kg of another alloy which has 90% silver by weight, the resulting alloy will have 84% silver by weight. Then, the weight of the initial alloy, in kg, is

1

###### Explanation

Let the weight of the alloy used be x kg and percentage of silver in it be k%.
According to the question:
(kx + 300)/(x + 3) = 90 …(i)
(kx + 180)/(x + 2) = 84 …(ii)
Solving (i) and (ii) we get, k = 80 and x = 3.

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