CAT Exam 2021 Slot 3 Solved Paper

Considering the distance travelled by Mira in one minute $= M$, The distance traveled by Amal in one minute $= A$. Given if they walk in the opposite direction it takes 3 minutes for both of them to meet. Hence $3 \times (A+M) = C$ $C$ is the circumference of the circle. Similarly, it is mentioned that if both of them walk in the same direction Amal completes 3 more rounds than Mira : Hence $45 \times (A-M) = 3C$ Multiplying $(1) \times 15$ we have : $45A + 45M = 15C$ $45A - 45M = 3C$ Adding the two we have A = $\frac{18C}{90}$ Subtracting the two M = $\frac{12C}{90}$ Since Mira travels $\frac{12C}{90}$ in one minute, in one hour she travels : $\frac{12C}{90} \cdot 60 =80C$ Hence a total of 8 rounds. Alternatively, Let the length of track be $L$ and velocity of Mira be $a$ and Amal be $b$ Now when they meet after 45 minutes Amal completes 3 more rounds than Mira. So we can say they met for the $3^{\text{rd}}$ time moving in the same direction so we can say they met for the first time after 15 minutes So we know - $\text{Time} \to \text{meet} = \frac{\text{Relative distance}}{\text{Relative velocity}}$ so we get -$\frac{15}{60} = \frac{L}{a \cdot b}$ Now When they move in opposite direction They meet after 3 minutes So we get - $\frac{3}{60} = \frac{L}{a + b}$ Dividing (1) and (2) We get - $\frac{a + b}{a - b} = 5$ or $4a = 6b$ or$a = \frac{3b}{2}$ Now substituting in (1) we get - $\frac{L}{b} \times 2 = \frac{15}{60}$ so, $\frac{L}{b} = \frac{1}{8}$ So we can say 1 round is covered in $\frac{1}{8}$ hours so in 1hour total rounds covered $= 8$.