The sum of two numbers is 100 and one number is two less than twice the other number. Then the numbers are...........
a) 12, 24
b) 34, 66
c) 102, -7
Solution:Let the two numbers be x and y.
Thus
x+y=100 and x=2y−2
Now substitute for x in the first equation and get 2y−2+y=100
3y−2=100 3y=102
y=34 and since they add to 100,
x=66
Answer should be 34,66
A train travels 360 km at a uniform speed. If the speed had been 5 km/h more, it would have taken 1 hour less for the same journey. Find the speed of the train.
a) 30 km/hr
b) 40 km/hr
c) 50 km/hr
d) 60 km/hr
Solution:Let x km/hr be the speed of train.
Time required to cover 360 km = 360/x hr.
As per the question given,
⇒ (x + 5)(360-1/x) = 360
⇒ 360 – x + 1800-5/x = 360
⇒ x2 + 5x + 10x – 1800 = 0
⇒ x(x + 45) -40(x + 45) = 0
⇒ (x + 45)(x – 40) = 0
⇒ x = 40, -45
Negative value is not considered for speed hence the answer is 40km/hr.
