
Elementary Math Fractions, Percentages, Word Problems, Equations, Inequations, Factorization, Expansion 
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July 2nd, 2018, 07:46 PM  #1 
Senior Member Joined: Aug 2014 From: India Posts: 310 Thanks: 1  How to solve this question completely?
at 22min 44 seconds, How to proceed the problem after finding the ratios: ? 24:72:20. after this ratios, what should I do? My sir skipped the solution at the end, Please tell the remaining part completely anyone. Last edited by Ganesh Ujwal; July 2nd, 2018 at 07:48 PM. 
July 3rd, 2018, 04:52 AM  #2 
Math Team Joined: Jan 2015 From: Alabama Posts: 3,261 Thanks: 894 
Frankly it is not clear to me what "ratios" you are referring to. But at about 22 minutes in the problem posted is "A, B, and C start a business with investments in the ratio of 0.125: 0.75: 0.25. After 8 months, A adds thrice and C withdraws half of his earlier investment. At the end of the year they earn a total profit of Rs 5,800. What should be B's share?" I have several problems with the statement of the problem. First, I would not call "0.125: 0.75: 0.25" a "ratio" at all! A ratio is a fraction it involves 2 things, not 3. The word "proportion" would be better here. Second, it is not clear what those numbers mean. In particular, they do not add to one so they are NOT fractions of the original investment. What is clear, I think, is that C's investment is twice A's and B's investment is 3 times C's so 6 times A's investment. Taking A's investment to be "x", C's is 2x and B's is 6x for a total amount invested of x+ 2x+ 6x= 9x. Their investments stayed that way for 8 months or 2/3 of the year. Then A "adds thrice". I assume that means that A add another 3x so his investment is now 4x. C withdrew half of his previous investment so his investment is now x. For the last 4 months or 1/3 of the year, their investments were A 4x, B 6x, and C x, for a total now of 11x. We can prorate those investments as (2/3)(9x)+ (1/3)(11x)= (29/3)x. The profit was 5800 so we can set (29/3)x= 5800, x= 3(5800)/29= 600. B's investment was 6x for the entire year so his share of the profits should be 6(600)= Rs 3600. (As a check, A invested x for 2/3 of the year then 4x for the last third so, prorated, A's investment was (2/3)x + (1/3)(4x) = (6/3)x = 2x. A's share of the profits should be 2(600) = Rs 1200. C invested 2x for 2/3 of the year and x for the last third so, prorated C's investment was (2/3)(2x) + (1/3)x = (5/3)x. C's share of the profits should be (5/3)(600)= Rs 1000. Those profits total to 3600 + 1200 + 1000 = Rs 5800.) Last edited by skipjack; July 3rd, 2018 at 09:24 AM. 
July 3rd, 2018, 05:18 AM  #3 
Math Team Joined: Jan 2015 From: Alabama Posts: 3,261 Thanks: 894 
At 24 minutes the problem is "P and Q started a business by investing Rs 45000 and Rs 54000 respectively. After 4 months R joined the business with a capital of Rs 40000. After 2 more months Q left the business with his capital. At the end of the year P got Rs 13,500 as his share in the profit. What was the total profit earned?" Again this is ambiguous. "Q left the business with his capital". Does that mean that Q does not receive any of the profit at the end of the year? That does not seem fair to me so I am going to assume that P, Q, and R all share in the profits in the ratio in which they had money invested. P had Rs 45,000 invested the entire year. Q had Rs 54,000 invested 1/2 year. R had Rs 40,000 invested 2/3 of the year. There was a total of 45000+ (54000/2)+ (40000)(2/3)= 45000+ 27000+ 80000/3= (135000+ 81000+ 80000)/3= 296000/3 invested. P had Rs 54000 invested the entire year so his share was 54000/(296000/3)= 0.547 or 54.7%. His profit, Rs 13,500, must be 54.7% of the total profit. Calling the profit "P", 0.547 P= 13500 so P= 13500/0.547= Rs 24,680. 
July 3rd, 2018, 09:26 AM  #4 
Global Moderator Joined: Dec 2006 Posts: 19,521 Thanks: 1747 
After 8 months (2/3 of a year), A adds thrice his earlier investment, so A effectively had twice his earlier investment throughout the year (because 0.125(2/3) + 0.375(1/3) = 0.25). A similar calculation for C gives his effective contribution as 0.25(2/3) + 0.125(1/3) = 5/24. Splitting 5,800 into 3 parts in the ratios 0.25 : 0.75 : 5/24 gives 1200 : 3600 : 1000, so B's share of the total profit should be Rs 3,600. 
July 3rd, 2018, 11:56 AM  #5  
Math Team Joined: Oct 2011 From: Ottawa Ontario, Canada Posts: 13,119 Thanks: 913  Quote:
(look at it as savings accounts earning same rate) P invested 45000, received 13500 after 1 year: translates to 2.5% per month. Q invested 54000 for 6 months: 54000(.025)(6) = 8100 R invested 40000 for 8 months: 40000(.025)(8) = 8000 Total = 13500 + 8100 + 8000 = 29600 Last edited by Denis; July 3rd, 2018 at 12:12 PM.  

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