CBSE Class 10 Sample Paper for 2020 Boards - Maths Standard

Class 10
Solutions of Sample Papers for Class 10 Boards

## A train covers a distance of 360 km at a uniform speed. Had the speed been 5 km/hour more, it would have taken 48 minutes less for the journey. Find the original speed of the train.

Note : This is similar to Ex 4.3, 8 of NCERT – Chapter 4 Class 10

### Transcript

Question 37 (OR 1st question) A train covers a distance of 360 km at a uniform speed. Had the speed been 5 km/hour more, it would have taken 48 minutes less for the journey. Find the original speed of the train. Let the speed of train be x km/hr Normal speed Distance = 360 km Speed = x km/hr Speed = π·ππ π‘ππππ/ππππ x = 360/ππππ Time = 360/π₯ Speed 5 km/h more Distance = 360 km Speed = (x + 5) km/hr Time = (360/π₯ " β " 48/60) hours Speed = π·ππ π‘ππππ/ππππ x + 5 = 360/((360/π₯ " β " 48/60) ) (x + 5) (360/π₯ " β " 48/60) = 360 From (1) (x + 5) (360/π₯ " β " 48/60) = 360 (x + 5) (360/π₯ " β " 4/5) = 360 (x + 5) ((5 Γ 360 β 4π₯)/5π₯) = 360 (x + 5) ((1800 β 4π₯)/5π₯) = 360 (x + 5) (1800 β 4x) = 360 Γ 5x x(1800 β 4x) + 5(1800 β 4x) = 1800x 1800x β 4x2 + 5(1800) β 20x = 1800x 1800x β 4x2 + 9000 β 20x = 1800x 1800x β 4x2 + 9000 β 20x β 1800x = 0 β 4x2 β 20x + 9000 = 0 4x2 + 20x β 9000 = 0 4(x2 + 5x β 2250) = 0 x2 + 5x β 2250 = 0 Comparing with ax2 + bx + c = 0 a = 1, b = 5, c = β2250 Roots of the equation are given by x = (β π Β± β(π^2 β 4ππ))/2π Putting values x = (β5 Β± β(5^2 β 4 Γ 1 Γ (β2250) ))/(2 Γ 1) x = (β5 Β± β(25 + 4 Γ 2250 ))/2 x = (β5 Β± β(25 + 9000))/2 x = (β5 Β± β9025)/2 x = (β5 Β± β(5^2Γγ19γ^2 ))/2 x = (β5 Β± 5Γ19)/2 x = (β5 Β± 95)/2 x = (β5 + 95)/2 x = 90/2 x = 45 x = (β5 β 95)/2 x = (β100)/2 x = β50 Hence x = 45, x = β50 are the roots of the equation We know that Speed of train = x So, x cannot be negative β΄ x = 45 is the solution So, Speed of train = x = 45 km/hr