CAT 2024 Question Paper | Quant Slot 2

CAT Questions

CAT 2024 Quant was dominated by Algebra followed by Arithmetic. In Arithmetic, the questions were dominated by topics like Speed-time-distance, Mixture and Alligations. This year, there was a surprise. The questions from Geometry were relatively on the lower side as compared to the previous years. There were 8 TITA Qs this year. Overall this section was at a medium level of difficulty.

Question 10 A company has 40 employees whose names are listed in a certain order. In the year 2022, the average bonus of the first 30 employees was Rs. 40000, of the last 30 employees was Rs. 60000, and of the first 10 and last 10 employees together was Rs. 50000. Next year, the average bonus of the first 10 employees increased by 100%, of the last 10 employees increased by 200% and of the remaining employees was unchanged. Then, the average bonus, in rupees, of all the 40 employees together in the year 2023 was

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Video Explanation

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Explanatory Answer

Let 'a' be sum of bonuses of 1 st 10 employees, ' $b$ ' be the sum of bonuses of $2^{\text {nd }} 10$ employees, ' $c$ ' be the sum of bonuses of $3^{\text {rd }} 10$ employees and ' $d$ ' be the sum of bonuses of last 10 employees. $$\begin{array}{l} a+b+c=40 k \text { * } 30=1200 k----- \text { (1) } \\ b+c+d=60 k * 30=1800 k-------(2) \\ a+d=50 k * 20=1000 k-----------(3) \end{array}$$ Adding the three equations we get, $$\begin{array}{l} 2 a+2 b+2 c+2 d=4000 k \\ a+b+c+d=2000 k . \\ a=200 k \\ d=800 k \\ b+c=1000 k \end{array}$$ In 2023, the average bonus of the first 10 employees increased by $100 \%$. $$a=200 k+200 k=400 k$$ In 2023, the average bonus of the last 10 employees increased by $200 \%$. $$d=800 k+800 k+800 k=2400 k$$ Average in the year 2023 $=(400 k+1000 k+2400 k / 40)=3800 k / 40=380 k / 4=95000$

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The question is "A company has 40 employees whose names are listed in a certain order. In the year 2022, the average bonus of the first 30 employees was Rs. 40000, of the last 30 employees was Rs. 60000, and of the first 10 and last 10 employees together was Rs. 50000. Next year, the average bonus of the first 10 employees increased by 100%, of the last 10 employees increased by 200% and of the remaining employees was unchanged. Then, the average bonus, in rupees, of all the 40 employees together in the year 2023 was"

Hence, the answer is '95000'

Choice B is the correct answer.

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