Question

solve the following question

Answer 1

Let the speed of A and B be x km/hr and y km/hr respectively.

time taken by A to cover 30 km = 30/x hrs.
time taken by B to cover 30 km = 30/y hrs.
 
according to the question,
30/x - 30/y = 3
10/x - 10/y = 1.......eq.1 

if A doubles his pace,then the speed of A is 2x km/hr.
 therefore time taken by A to cover 30 km = 30/2x hrs. 
and time taken by B to cover 30 km = 30/y hrs. 

according to the question,
30/y - 30/2x = 3/2
10/y - 5/x = 1/2
-10/x + 20/y = 1......eq.2

now assume 1/x = u and 1/y = v
putting the vale in eq. 1 and 2
10u - 10 v = 1......eq.3
 -10u + 20 v = 1 ....eq.4

adding eq.3 and 4,
we get
10v=2
 v = 1/5

putting v = 1/5 in eq.3,
 we get
10u - 3 = 0
u = 3/10 

now, u = 3/10 = 1/x 
x = 10/3.
and v = 1/5 = 1/y
 y = 5 
ans. speed of A and B are 10/3 km/hr and 5 km/hr respectively.