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In the question of the Shopping Mall escalator floor 1 to 5: I expected another approach which would be realizing that the speeds under the given conditions are always in AP (M+E, M, M-E), so the time taken under the circumstances will be in HP and the answer will be the harmonic mean of the given time values.
In last ques n=15 b took 8 step so remaining steps are 7 which are taken by escalator so It will be e*tb=7 Similarly for c remaining steps are 10 So e*tc=10 By equating we get tb:tc=7:10
Alternate way to solve Q1: Speed of P in case 1 = 25 steps / 30 sec = 5/6 steps/sec Speed of escalator = e (let) Thus, (5/6 + e)x(30) = N [speed x time = dist] Speed of P in case 2 = 5/2 steps/sec (since it is tripled) So: (5/2 + e)x(18) = N Equate and solve for e….. turns out e = 5/3 steps/sec Put e in any one of the above 2 eqns to get N = 75 steps.
Solved the 5:57 question by AP & HP method, Speed can be considered M+E, M, M-E for time 36sec, ? , 108sec , since speeds are in AP, time will be in HP so the time when escalator is not moving can be calculated by b=2ac/a+c . Answer is also same (54secs) is this also correct?
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In the question with A and B moving together, A takes 25 steps to reach the top while B takes only 20. But we have taken speed as A= 3x/second and B=2x per . Ideally, higher is the speed, time taken should be lesser right? Is this the right approach?
Yes, the approach is right. The case you have mentioned is when 'D' is constant, here the distance or steps taken by A and B are different. So, when escalator is switched off N(A)= 50 and N(B)= 60 which means B would have already taken 10 steps before A walked up in escalator that's why even though their steps ratio was 3:2 B reached early to the top. Not given that they walked up on escalator together. hope this ans will help you.
@@swatibisht4572 N = 50 for both A and B. (From your comment, N(B)=60 is incorrect.) Therefore, B did not get a head start. Even if 'D' is constant and they start together, the person with higher speed (A in this case) will always climb more steps. E.g. A → 3 steps/sec B → 2 steps/sec E --> 1 step/sec (constant, same for both A and B) N = Time x Effective speed (A+E or B+E) A x Time for A = Steps covered by A B x Time for B= Steps covered by B E x Time for A or B = Steps covered by E with A or B Substitute any value of D (i.e., Number of steps), e.g., N = 12, 24, 48 etc, the number of steps taken by A will always be greater than B (even though time taken by A to reach the top will be less) because speed of A is greater than B, and E is same for both of them. The confusion arises if you misinterpret 3 steps/sec as 1 hop for A. (And 2 steps/sec as 1 hop for B) Ofcourse, if we were to consider hops, A will hop fewer times than B to reach the top. But if we consider steps/sec, 3 steps/sec literally and mathematically means the person has climbed 3 steps in 1 sec (even though A might have skipped 2 steps and hopped onto the 3rd step).
@@niloychakravorty3832 M+E ,M ,M-E are the speeds and they are in AP., therefore their time is in HP . now T {M+E}= 36 T{M-E} = 108 , Therefore T{M} = 2*36*108 / 36+108 = 54
The H.P concept has made all these problems a piece of cake, I would earlier try to use relative speeds and then stare at my notebook looking to reduce that one extra variable.
Sir, in Q3 (15:00) if speed of A:B is 3:2, why can we not solve the question considering the time taken ratio as 2:3? If time taken by A is (2x/5), assuming x is the total time taken Na = 25 + (2x/5)E Nb = 20 + (3x/5)E On solving we get xE = 25 On substituting xE in any one of the equation we get N = 35. Why does this approach not give the same answer?
Because this approach is only used when both the people are travelling the same distance but here A takes 25 steps whereas B takes 20 steps and hence they are not travelling the same distance
17:47 how much steps will taken by b ? I did like this Steps taken by A =25+25E/3 and B=20+10E by solving this i am getting E= 11/3 and putting 11/3 in equation of A giving 50 steps but B giving 56.66 steps . But according to sir if you will put the value in b you are getting same steps.? How
How did we get the time taken by escalator as 25/3x ? The speed taken should also constitute the speed of the escalator. Even though the speed of the escalator is constant, why we haven't added the speed of the escalator to the speed of the person A. 25/3x will only give us the time taken by the person
Hi Sir, I have a doubt. In the last question, why have we not considered the relative speed (x-e) but just x when put it equal to (10/ta) in A white moving up or down for that matter?
if N is no of step when it is switched off then why do we write the equation of N = no of man step + escalator step. Logically it shouldn't be this then ?
Please help with this question sir Pavan walked up a descending escalator (a moving staircase) and took 154 steps in 100 seconds to reach the top. Rishabh started simultaneously from the top and taking 3 steps for every 4 taken by Pavan, reached the bottom in 40 seconds. How many steps from the bottom were Pavan and Rishabh, when they crossed each other?
Total steps = N Speed of escalator = e ratio of PAWAN Speed to ratio of RISHAB'S is 4:3 SAY Pawan's speed = 4x Rishab's speed = 3x Overall effective time taken for total steps 'N': Case 1: (Pawan and escalator in opp. direction) N/(4x - e) =100 ...1 (Pawan- upwards) Case 2: (Rishab and escalator in same. direction) N/(3x+e) = 40 .....2 (Rishab- downwards) we know Pawan took 100s to take 154steps ...hence pawan speed,4x = 154/100 x =77/200 Solving 1 and 2 by x value, we get N = 77 and e = 77/100 they will cross each other after (total distance /individual speeds) secs i.e., 77/(4x+3x) seconds, i.e., 200/7 seconds Number of steps from bottom = (4x-e) *200/7 = 22 steps Number of steps from top = (3x + e) *200/7 = 55 steps
@@kunalsingh6423 Instead of using Harmonic you can go with AP method by using effective speed funda. Take speeds as M/36 +1, M/t , M/108-1. These three speeds are in AP. Calculate difference between M/36-1 and M/108-1 and divide it by 2. Add this difference to M/108 -1 and equate to M/t. You will get 54 seconds.
@@kunalsingh6423 3 speeds - M+E, M, M-E are in A.P. since their common difference is E. Therefore, the time taken will be in HP. So, the HM of the 3 quantities will be - 2ab/a+b. Solve and you'll get the answer. All the best
In the second last question, where A and B are moving up escalator why have we taken their speed to be 3x:2x. Why do we require x when we know the exact quantity?
A takes 3 steps for every 2 of B's steps which means if B takes 4 steps, A will take 6 steps and similarly if B 6 steps then A 9 steps. So we only know their ratio not the actual values.
Because distance is not constant. While the Total distance i.e.the no.of steps on escalator is constant, individually A and B don't cover equal distances
Sir.....last Question me ik ratio nikala hai yeslea tb & tc consider kia hai......but sir agar ( 8 / tb ) & ( 5/ tc ) lekar solve karne par mera answer same ni aa raha......mujhe bas reason jaana tha aisa kyu ho raha hai 😭
nvm I got it. Inke steps same nahi hai B ke 8 and C ke 5. THerefore, Distance is not contant, hence if speed is 16:7, time cannot be 7:16. For time of B, divide no of steps(8) by speed (16) and same for C. The answer will be 7:10
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