41. | | A is twice as fast as B and B is thrice as fast as C is. The journey covered by C in 54 min will be covered by B in : | | (a)18 min | | (b)27 min | | (c)38 min. | | (d)9 min. |
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Answer is: ALet C's speed = X kmph Then, B's speed = 3X kmph and A's speed = 6X kmph.
Ratio of the speed of A, B and C = 6X : 3X : X = 6 : 3 : 1
Ratio of time taken = 1/6 : 1/3 : 1 = 1 : 2 : 6
If C takes 6 min, then B takes 2 min
If C takes 54 min, then B takes (2/6) x 54 min. = 18 min.
42. | | Two cars P and Q start at the same time from A and B which are 120 km. If the two cars travel in opposite directions, they meet after one hour and if they travel in same direction (from A toward B), then P meets Q after 6 hours. What is the speed of car P ? | | (a)60 kmph | | (b)70 kmph | | (c)120 kmph | | (d)Data inadequate |
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Answer is: BLet their speeds be X kmph and Y kmph respectively.
Then, 120/(X+Y) = 1
X + Y = 120 →(1)
Now, when they move in same direction :
(Distance travelled by P in 6 hours) - (Distance travelled by Q in 6 hours) = 120 km.
6X - 6Y = 120
X - Y = 20 →(2)
On solving (1) and (2) ,
X = 70
Y = 50
P's speed = 70 kmph.