Question

we euclid's algorithm to find the HCF of 4012 and 12576.

Answer 1

12576=
4012×3+546
4012=546×7+190
546=190×2+166
190=166×1+24
166=24×7+0
HCF is 24

Answer 2

$\huge\mathcal\colorbox{blue}{{\color{cyan}{ANSWER☆~~~}}}$

Let us say, the average speed of passenger train = x km/h.

Average speed of express train = (x + 11) km/h

Given, time taken by the express train to cover 132 km is 1 hour less than the passenger train to cover the same distance. Therefore,

(132/x) – (132/(x+11)) = 1

132(x+11-x)/(x(x+11)) = 1

132 × 11 /(x(x+11)) = 1

⇒ 132 × 11 = x(x + 11)

⇒ x2 + 11x – 1452 = 0

⇒ x2 + 44x -33x -1452 = 0

⇒ x(x + 44) -33(x + 44) = 0

⇒ (x + 44)(x – 33) = 0

⇒ x = – 44, 33

As we know, Speed cannot be negative.

Therefore, the speed of the passenger train will be 33 km/h and thus, the speed of the express train will be 33 + 11 = 44 km/h.