CAT 2021 Question Paper | Quant Slot 3

CAT 2021 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 3 : Mira and Amal walk along a circular track, starting from the same point at the same time. If they walk in the same direction, then in 45 minutes, Amal completes exactly 3 more rounds than Mira. If they walk in opposite directions, then they meet for the first time exactly after 3 minutes. The number of rounds Mira walks in one hour is

Video Explanation

Explanatory Answer

Let ‘a’ be the number of minutes required by Amal to complete one round,
and ‘m’ be the number of minutes required by Mira to complete one round.
In 45, minutes, number of rounds completed by Amal = \( \frac { 45 } { a } \)
In 45, minutes, number of rounds completed by Mira = \( \frac { 45 } { m } \)
We know that, in 45 minutes, Amal completed 3 more rounds than Mira.
Therefore, \( \frac { 45 } { a } \)= \( \frac { 45 } { m } \)+ 3
\( \frac { 45 } { a } - \frac { 45 } { m } = 3 \)
\( \frac { 1 } { a } - \frac { 1 } { m } = \frac { 1 } { 15 } \)— (1)
In 3, minutes, number of rounds completed by Amal = \( \frac { 3 } { a } \)
In 3, minutes, number of rounds completed by Mira = \( \frac { 3 } { m } \)
We know that, in 3 minutes, Amal and Mira together complete one round.
Therefore, \( \frac { 3 } { a } \)+ \( \frac { 3 } { m } \)= 1
\( \frac { 1 } { a } + \frac { 1 } { m } = \frac { 1 } { 3 } \)— (2)
(2) - (1) = \( \frac { 1 } { a } + \frac { 1 } { m } - \frac { 1 } { a } + \frac { 1 } { m } = \frac { 1 } { 3 } - \frac { 1 } { 15 } \)
\( \frac { 2 } { m } = \frac { 4 } { 15 } \)
\( \frac { 1 } { m } = \frac { 2 } { 15 } \)
m = \( \frac { 15 } { 2 } \)
So, Mera needs \( \frac { 15 } { 2 } \)minutes to complete 1 round.
She needs 15 minutes to complete 2 rounds and
60 minutes to complete 8 rounds.
So Meera covers 8 rounds in 1 hour.

The answer is '8'

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