00:00If x number of workers of the same strength work 6 hours a day, they can complete half the job in 10 days.
00:05If Y workers, working 5 hours a day, can complete 1/5 of the same job in 9 days, then what is x plus y?
00:11The question asks for the minimum value of the total.
00:14Now, when we set up our proportion, friends, what is x workers?
00:20What's so special about working 6 hours a day, guys?
00:24How much can you guys make in 10 days?
00:30Half the job.
00:32Let A divided by 2 be the work.
00:33A is half the job.
00:35So, what does y number of workers represent, folks?
00:39I work 5 hours a day, writing the same data under the same other data, while I'm setting up the proportions.
00:47What's up, guys?
00:491/5 of the same job in 9 days.
00:55A divided by 5 work.
00:58According to what they did, we need to find the minimum value of the sum of x plus y.
01:03But before we find that, there's the principle of compound proportionality here, right guys?
01:11What is compound proportion, you'll remember it in these kinds of questions.
01:14When we ratioed the things here, the ratio of a/2 to a/5 was equal to the ratio of the products of the other same-side data.
01:27x times 6 times 10 divided by y times 5 times 9 equals...
01:32Divide by 3 = 2, divide by 3 = 3, divide by 5 = 1, divide by 5 = 2 (in multiplication and division).
01:39Because of that.
01:40That equals 4 times x divided by 3 times y.
01:44a divided by 2 multiplied by inverted multiplied by you'll remember the numbers from fractions.
01:495 divided by a.
01:50That's also equal to 4 times x divided by 3 times y, right?
01:54Yes, the 'a's cancel each other out.
01:55It's 5 divided by 2.
01:57If you do cross-multiplication, it's 15 times y, right guys?
02:02Yes.
02:03That's equal to 8 times x.
02:05How do you count between 15 and 8, friends?
02:07They are considered relatively prime.
02:09Therefore, if you say y is 8k, you must say x is 15k, which is a multiple of 15.
02:18Since K is also a worker here, we need to have all the friends present.
02:24Why?
02:24It must be a positive natural number, not zero.
02:28In this case, since the question asks for the minimum value of x plus y, we find it as 8k plus 15k, which equals 23k.
02:36So what is the smallest of our natural numbers that is different from zero?
02:39What is 1?
02:4223 multiplied by k equals 23, which is the minimum we can find.
02:46Our answer is "perforated".
02:47Translation and Subtitles by M.K.
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