CAT 2022 Question Paper (Slot 1) - Quant 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 $$x=\frac{3D}{5}$$
$$\frac{x}{b}=9$$
$$\frac{3D}{b\times5}=9$$
$$\frac{D}{b}=15$$
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
SHIVA PENDEM
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
derstand
Aman Lalwani
11 months, 1 week ago
Not clearly explaining the ratio portion after they met