question_answer

Places M and N are 90 km apart from each other on a national highway. A truck starts from M and another from N at the same time. If they go in the same direction, then they meet in 9 hours and if they go in opposite directions they meet in - hours. The speed of the trucks are ____.  

A)  90 km/hr, 40 km/hr               

B)  40 km/hr, 30 km/hr                

C)  20 km/hr, 60 km/hr              

D)  50 km/hr, 12 km/hr              

Correct Answer: B

Solution :

Let x km/hr be the speed of truck starting from M and y km/hr be the speed of truck starting from N.                                       Case I: If they meet at P.                                Speed \[=\frac{Distance}{Time}\] For M, \[x=\frac{90+a}{9}\] or\[9x=90+a\]             For N, \[y=\frac{a}{9}\]  or  \[9y=a\]                      \[\Rightarrow \]   \[10+y=x\]                        ...(1) Case II: If they meet at P.                 For M, \[x=\frac{a}{9/7}\] and For N, \[y=\frac{9-a}{9/7}\] \[\Rightarrow \]  \[70=x+y\]                        ...(2) Solving (1) and (2), we get \[y=30\text{ }km/hr\]and \[x=40\text{ }km/hr\]