This "HARD"problem belongs to Ratio and Algebra
Kaushal is playing on the reliance mall escalators. One escalator goes up, one goes down, and one is out of service; otherwise, they're all identical. The up and down escalators go at the same speed. You can assume that Kaushal always runs at the same speed.
Kaushal can run up the up escalator in seconds. He can run up the down escalator in seconds. How long does it take him to run up the out-of-service escalator?
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1 solution
So now assume speed of "Kaushal" = B/sec.
And "Escalator" speed = E/sec.
Now in problem they said that all escalator's are identical which means all escalator's have same length.
So now what is the speed of Kaushal when he is running up the run up escalator B+E/sec so now what is the length of run up escalator = (B+E/sec)*6 so length of run up escalator = 6B+6E.
So now what is the speed of Kaushal when he is running up the run down escalator B + -E/sec so now what is the length of run down escalator is (B+-E/sec)*30 so length of run down escalator = 30 + -30E.
So now algebra $6B+6E$ $=$ $30B+-30E$.
= 6B+6E+30E = 30B+-30E+30E
= $6B+36E$ = $30B
= $6B+36E+-6B = 30B+-6B
= 36E = $24B
= 3E = 2B
So now all escalator length is 6B+6E = 6B+4B = 10B.
LENGTH OF ESCALATOR = 10B. SPEED OF Kaushal = B/SEC. TIME TAKEN = 10SEC.
So finally the time to run up the out of service escalator is = 10seconds.