144144 wrote:
Karishma, can u explain ur system in more details plz?
y produces 20% faster so as far as i understand
if x produces 5
Y produces 6/5
in one hour.
hmm - im stuck. ill be happy to learn ur way - ur ways are amazing. thanks.+1
What I use a lot is ratios. Ratios eliminate the need for equations.
In different questions, you will need to handle data differently to get a ratio.
e.g.
1.
Speed of x is 40 m/hr and speed of y is 60 m/hr.
Then ratio of speeds is 40:60 i.e. 2:3 (lowest representation - in ratios 2:3 is same as 4:6 which is same as 20:30 etc)
2.
Speed of x is 20% more than that of y.
If speed of y is 1, speed of x is 6/5 (i.e. 20% = 1/5 more than 1). Ratio of speed of X:Y = 6/5:1 or 6:5 (Multiplying the ratio by 5) or simply, since speed of x is more, x will be 6 and y will be 5.
Now, quantities such as time, rate and work done are related to each other.
We know W = R*T
If two machines A and B with rates of work in the ratio 6:5 work for 1 hr each, who will do more work?
Since they are both working for the same time, A will do more work since its rate is higher. How much more work will A do as compared to B? Since A's rate is 20% higher, A will do 20% more work...
Now, let me ask you this - if both A and B do the same amount of work, who will take less time?
Since A's rate is 20% more, A will take less time. How much less time will it take? Let's say there was 30 units of work that each did.
A's rate - 6 units/hr, time taken - 30/6 = 5 hrs
B's rate - 5 units/hr, time taken - 30/5 = 6 hrs
So basically time taken flips the speed (time is inversely proportional to speed)
Time taken by A:B = 5:6
Now think, I tell you that A takes 10 hrs to do a job. How long will B take to do the same job? 12 hrs because they take time in the ratio 5:6.
Now, if I tell you that for a particular work, difference between time taken by A and time taken by B is 10 hrs. How long did A take to finish the job?
Since the difference between the times should be 10, they must have taken 50 and 60 hrs to do the work.
These are a few concepts that we use to solve questions using ratios. The next topic I am taking up on my
Veritas blog is ratios. Watch out for the first post early next week... It should make these concepts clearer...
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Karishma
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