# CBSE Class 10 Math Question Paper 2018 | Q23B

###### CBSE Solved Question Paper 4 Mark | Quadratic Equations

Question 23B: A train travels at a certain average speed for a distance of 63 km and then travels a distance of 72 km at an average speed of 6 km/hr more than its original speed. If it takes 3 hours to complete total journey, what is the original average speed?

## NCERT Solution to Class 10 Maths

### Explanatory Answer | CBSE Class 10 Math Board Paper 2018 Q23B

Distance for 1st part = 63 km
Let the average speed for this part of the journey be s km/hr

Distance covered in 2nd part = 72 km
Average speed for 2nd part is 6 km/hr more than the first part.
i.e., Average speed for 2nd part = (s + 6) km/hr

Total time taken = 3 hr
Let the time taken for 1st part be t hr
∴ Time taken for second part = (3 - t) hr

Part 1 journey → s × t = 63 -----(1)
Part 2 journey → (s + 6) (3 - t) = 72 -----(2)

From (1) t = $$frac{63}{s}$ Substitute t = $\frac{63}{s}$ in$2)
(s + 6) (3 - $$frac{63}{s}$) = 72$s + 6) ($$frac{3s - 63}{s}$) = 72$s + 6) (3s - 63) = 72s
3s2 - 63s + 18s - 378 = 72s
3s2 - 117s - 378 = 0

Divide the equation by 3
s2 - 39s – 126 = 0
s2 - 42s + 3s – 126 = 0
(s - 42) (s + 3) = 0
s = 42 or s = -3

Speed has to be positive.
∴ Original average speed = 42 km/hr

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