Book: RS Aggarwal - Mathematics
Chapter: 10. Quadratic Equations
Subject: Maths - Class 10th
Q. No. 45 of Exercise 10E
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A train covers a distance of 480 km at a uniform speed. If the speed had been 8 km/hr less then it would have taken 3 hours more to cover the same distance. Find the usual speed of the train.
Let the usual speed of the train be x km/h
Reduced speed of the train = (x – 8) km/h
Distance of journey = 480km
Time taken to reach destination at usual speed = 
Time taken to reach destination at reduced speed = 
According to given question
x2 – 8x = 1280
x2 – 8x – 1280 = 0
Using the splitting middle term – the middle term of the general equation 
is divided in two such values that:
Product = a.c
For the given equation a = 1 b = – 8 c = – 1280
= 1. – 1280 = – 1280
And either of their sum or difference = b
= – 8
Thus the two terms are – 40 and 32
Difference = – 40 + 32 = – 8
Product = – 40.32 = – 1280
x2 – 40x + 32x – 1280 = 0
x (x – 40) + 32(x – 40) = 0
(x – 40)(x + 32) = 0
x = 40 or x = – 32
x = 40 (speed cannot be negative)
Hence the usual speed of the train is 40 km/h
minutes. If one pipe takes 3 minutes more than the other to fill it, find the time in which each pipe would fill the cistern.
