CAT 2022 Question Paper (Slot 1) - Quant Question 5

Question 5

Trains A and B start traveling at the same time towards each other with constant speeds from stations X and Y, respectively. Train A reaches station Y in 10 minutes while train B takes 9 minutes to reach station X after meeting train A. Then the total time taken, in minutes, by train B to travel from station Y to station X is


M - First meeting point

Let the speeds of trains A and B be 'a' and 'b', respectively.

$$\frac{x}{a}=\ \frac{\ D-x}{b}$$

It is given,

$$\frac{D}{a}=10$$ and $$\frac{x}{b}=9$$

$$\frac{x}{\frac{D}{10}}=\ \frac{\ D-x}{\frac{x}{9}}$$

$$\frac{10x}{D}=\ \frac{\ 9D-9x}{x}$$

$$10x^2=\ \ 9D^2-9Dx$$

$$10x^2+9Dx-9D^2=\ 0$$

Solving, we get $$x=\frac{3D}{5}$$




The total time taken by train B to travel from station Y to station X is 15 minutes.

The answer is option B

View Video Solution


aditya goel

1 week ago

worst explanation


2 months, 1 week ago

only video explanation was excellent

Parul Singh

5 months, 2 weeks ago

how (P+15) (P-6), I understood the formula (a+b) (a-b) but how 15 and 6

sandeep sandy

3 months, 3 weeks ago

(p+15) = 0 and (p-6) = 0 sp p = -15 and p = 6

keshab giri

5 months, 3 weeks ago

Thank you

Dishant Makwana

5 months, 3 weeks ago

not un

Aman Lalwani

11 months, 1 week ago

Not clearly explaining the ratio portion after they met


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