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

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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.

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