1. Three runners A,B and C run a race,with runner A finishing 24 meters ahead of runner B &36 metres ahead of runner C ,while runner B finishes 16 metres ahead of runner C . Each runner travels the entire distance at a constant speed. What was the length of the race? A. 72 m B. 96 m C. 120 m D.144 m 2. A & B walk up an escalater (moving stairways). The escalator moves at a constant speed, A takes 6 steps for every 4 of B's steps. A gets to the top of the escalator after having taken 50 steps , while B (because his slower pace lets the escalator to do a little more of the work) takes only 40 steps to reach the top . If the escalator were turned off ,how many steps would they have to take to walk up? A. 80 B. 100 C. 120 D. 160 3.The owner of an art shop conducts his business in the following manner. Every once in a while he raises his prices by X%, then a while later he reduces all the new prices by X% . After one such up-down cycle, the price of the painting decreased by Rs. 441 . After a second up-down cycle ,the painting was sold for Rs. 1944.81. What was the original price of the painting? A.2756.25 B. 2256.25 C. 2500 D. 2000 |
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ANSWER to QN1) = 96 m
For every 6 steps of A , B takes 4 steps
=> For every 1 steps of A , B takes 2/3 steps
Let A takes 1 step/second and the stairways moves x steps up /second
To cross 50steps A would take 50 minutes and during that time the stairway would move 50x steps
Time taken to cross 40 steps = 40/(2/3) seconds = 60 seconds
Thus total number of steps = 100
n/a
Each time a cycle of increase and decrease in the price completes it follows the same pattern.
i.e. If the initial price is y, the price after one cycle would be y ( 1 - ( x /100 )^2 ).
So after one cycle
y ( x / 100 )^2 = 441...................... ( i )
Similarly after second cycle :
( y - 441 ) ( 1 - ( x /100 )^2 ) = 1944.81............ ( ii )
From solving equation ( i ) and ( ii ) we get :
The initial price ( y ) = 2756.25
thanks a lot
ya ,the answers are correct.
but i coudnt get the statement no.1,can u plz explain it.
hello
plz provide detailed solution to q. 1
Let x = the distance
When A covers distance x, B covers distance x – 24 and C covers distance x – 36.
Velocity of B/Velocity of C = Vb/Vc = (x-24)/(x-36)
When B covers distance x and C covers distance x – 16.
Velocity of B/Velocity of C = Vb/Vc = x /(x-36)
Comparing above two eqns
(x – 24)/( x – 36) = x / (x – 16)
=> -40x + 24*16 = -36x
=> 4x = 24 * 16
=> x = 96
n/a
thanks nishit
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