There are three cities A, B and C, not on the same straight road.
Two buses P and Q start simultaneously from A and B respectively
towards C. By the time Q reaches C, P is exactly halfway to C.
Immediately after Q reaches C, it starts travelling towards A and it
crosses P at a point 165 km from A. The ratio of the speeds of P and
Q is 3 : 5. Assume that the roads joining A to C, B to C and B to A
are all straight roads. If B is twice as far as from A as it is from C
and P would take to cover the distance from A to B, how much
time would Q take to cover the distance from C to A?
(1)2 2/5 hours
(2) 3 hours
(3) 3 3/5 hours
(4) 4 hours
Answers
Answer:
3 3/5 Hrs
Option 3 is right answer
Step-by-step explanation:
There are three cities A, B and C, not on the same straight road.
Two buses P and Q start simultaneously from A and B respectively
towards C. By the time Q reaches C, P is exactly halfway to C.
Immediately after Q reaches C, it starts travelling towards A and it
crosses P at a point 165 km from A. The ratio of the speeds of P and
Q is 3 : 5. Assume that the roads joining A to C, B to C and B to A
are all straight roads. If B is twice as far as from A as it is from C
and P would take to cover the distance from A to B, how much
time would Q take to cover the distance from C to A?
(1)2 2/5 hours
(2) 3 hours
(3) 3 3/5 hours
(4) 4 hours
missing information
and P would take to cover the distance from A to B - its 10 Hrs
Let say Speed of Bus P = 3x kmHr
Speed of Bus Q = 5x km/Hr
Let say in time t1 hr Q reaches from B to C
5xt1 = BC ( distance = Speed * Time)
3xt1 = AC/2 ( Q bus reaches half of AC in same time )
5xt1/3xt1 = BC/(AC/2)
=> 5/3 = 2BC/AC
=> 5AC = 6BC
let say after t2 he time Q & B crosses each other at AC (165 km from A)
5xt2 = AC - 165
3xt2 = 165 - AC/2
5xt2/3xt2 = (AC - 165)/(165 - AC/2)
=> 5/3 = (AC -165)/{(330 - AC)/2}
=> 5 (330-AC) = 6 (AC - 165)
=> 1650 - 5AC = 6AC - 990
=> 2640 = 11AC
=> AC = 240 km
5AC = 6 BC
=> BC = 5 * 240 / 6 = 200
BC = 200 km
BA = 2BC given
BA = 2 * 200 = 400
BA = 400 km
P take 10 hours from A t o B
P speed = 400 / 10
P speed = 40 km/Hr
P speed = 3x
3x = 40
x = 40/3
Q speed = 5x
Q speed = 5 * 40/3
Q speed = 200/3 km/Hr
Distance from C to A = 240 km
Time taken = 240/(200/3)
= 720/200
= 18/5 hrs
= 3 3/5 Hrs
Option 3 is right answer