2. Questions Bank
  3. 10th Class
  4. Mathematics
  5. Pair of Linear Equations in Two Variables

10th Class Mathematics Pair of Linear Equations in Two Variables Question Bank MCQs - Pair of Linear Equations in Two Variables

  • question_answer
    A train covered a certain distance at a uniform speed. If the train would have been 10 km/h faster, it would have taken 2 h less than the scheduled time and if the train was slower by 10 km/h, it would have taken 3 h more than the scheduled time. Then, the distance covered by the train is

    A) 50km

    B) 300km

    C) 600km

    D) 12km

    Correct Answer: C

    Solution :

    Let the actual speed of the train be x km/h and actual time taken be y h.
    We know that,
    Distance = Speed \[\times \] Time
    \[\therefore \] Distance = xy km
    According to the question,
    \[xy=\left( x+10 \right)\left( y-2 \right)\]
    \[\Rightarrow \,\,xy=xy-2x+10y-20\]
    \[\Rightarrow \,2x-10y+20=0\]
    \[\Rightarrow \,x-5y+10=0\]
    [dividing both sides by 2] ...(i)
    and  \[xy=\left( x-10 \right)\left( y+3 \right)\]
    \[\Rightarrow \,\,xy=xy+3x-10y-30\]
    \[\Rightarrow \,\,\,\,3x-10y-30=0\]                         … (ii)
    On multiplying Eq. (i) by 3 and then subtracting Eq. (ii) from it, we get
    \[3\times \left( x-5y+10 \right)-\left( 3x-10y-30 \right)=0\]
    \[\Rightarrow \,\,\,-5y=-60\]
    \[\therefore \,\,\,\,\,\,\,\,\,\,\,\,\,y=12\]
    On putting y = 12 in Eq. (i), we get
    \[x-5\times 12+10=0\]
    \[\Rightarrow \,\,\,\,x-60+10=0\]
    \[\Rightarrow \,\,\,\,x=50\]
    Hence, the distance covered by train
    \[xy=50\times 12=600\,km\]


You need to login to perform this action.
You will be redirected in 3 sec spinner