CAT 2022 Question Paper | Quant Slot 2

CAT 2022 Quant was dominated by Arithmetic followed by Algebra. 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 2 : Working alone, the times taken by Anu, Tanu and Manu to complete any job are in the ratio 5 : 8 : 10. They accept a job which they can finish in 4 days if they all work together for 8 hours per day. However, Anu and Tanu work together for the first 6 days, working 6 hours 40 minutes per day. Then, the number of hours that Manu will take to complete the remaining job working alone is

Video Explanation

Explanatory Answer

Time taken by Anu, Tanu and Manu to complete a job is in the ratio 5 : 8 : 10
This means that their efficiencies are in the ratio \( \frac { 1 } { 5 } : \frac { 1 } { 8 } : \frac { 1 } { 10 } \)
Or, their efficiencies are in the ratios 8 : 5 : 4
This means, for instance, if Anu can wash 8 plates in an hour, Tanu and Manu can wash 5 & 4 plates respectively in one hour.
So, let us remodel the entire question over this imaginary scenario of washing plates…
All three of them finish the job in 4 days working 8 hours per day.
Anu, Tanu and Manu can wash 8, 5 and 4 plates respectively in an hour.
So the total number of plates = \( ( 8 + 5 + 4 ) \times 4 \times 8 = 17 \times 4 \times 8 \)
Anu and Tanu work together for 6 days, working 6 hours 40 minutes per day.
The total number of plates washed by them = \( ( 8 + 5 ) \times 6 \times 6 \frac { 2 } { 3 } = 13 \times 40 \)
So the remaining plates to be washed \( = 17 \times 4 \times 8 - 13 \times 40 \)
\( = 4 ( 17 \times 8 - 130 ) \)
\( = 4 ( 80 + 56 - 130 ) \)
\( = 4 \times 6 \)
So, the question is, in how man hours can Manu wash \( 4 \times 6 \) plates?
We know that Manu can wash 4 plates in one hour.
Therefore, he requires 6 hours to wash \( 4 \times 6 \) plates.

The answer is '6'

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